MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

Instance: smallinvSNPr1b100-110

```Small Investor Mean-Variance Portfolio Optimization
This is a natural extension of the standard Markovitz Mean-Variance-Optimization
(MVO) model by constraints for small investors. The variables in the standard
Markovitz model determine which fraction of the investment is made in the
repective assets. When the investment is bounded within a range that is not very
much bigger than the prices of the assets, one has to take into account that
each asset has a minimum unit of which only integer multiples can be traded,
e.g. 1, 0.1, or 0.01. Hence, the optimization problem for the small investor has
integer variables in addition to the budget constraints that define lower and
upper bounds on the investment.
Update (2018-08-07): After a fix to the convexity check routines, it was found that
the smallest eigenvalue of the quadratic coefficients matrix in the quadratic constraint
is slightly negative (about -2e-7). Though these instances were originally intended to be
convex, a loss of precision in the process of creating the original POLIP instance lead to
a loss of positive semi-definiteness in the coefficients matrix.```
 Formatsⓘ ams gms lp mod nl osil pip Primal Bounds (infeas ≤ 1e-08)ⓘ 5.81307796 p1 ( gdx sol ) (infeas: 0) Other points (infeas > 1e-08)ⓘ Dual Boundsⓘ 4.38157755 (ANTIGONE)5.81307796 (BARON)5.81307796 (COUENNE)5.81307796 (LINDO)-0.99660118 (SCIP) Sourceⓘ POLIP instance portfolio/small-investor-MVO-SNP100-return_0.0010-budget_10000-11000 Applicationⓘ Portfolio Optimization Added to libraryⓘ 26 Feb 2014 Problem typeⓘ MIQCP #Variablesⓘ 101 #Binary Variablesⓘ 0 #Integer Variablesⓘ 100 #Nonlinear Variablesⓘ 100 #Nonlinear Binary Variablesⓘ 0 #Nonlinear Integer Variablesⓘ 100 Objective Senseⓘ min Objective typeⓘ linear Objective curvatureⓘ linear #Nonzeros in Objectiveⓘ 1 #Nonlinear Nonzeros in Objectiveⓘ 0 #Constraintsⓘ 4 #Linear Constraintsⓘ 3 #Quadratic Constraintsⓘ 1 #Polynomial Constraintsⓘ 0 #Signomial Constraintsⓘ 0 #General Nonlinear Constraintsⓘ 0 Operands in Gen. Nonlin. Functionsⓘ Constraints curvatureⓘ indefinite #Nonzeros in Jacobianⓘ 401 #Nonlinear Nonzeros in Jacobianⓘ 100 #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ 10000 #Nonzeros in Diagonal of Hessian of Lagrangianⓘ 100 #Blocks in Hessian of Lagrangianⓘ 1 Minimal blocksize in Hessian of Lagrangianⓘ 100 Maximal blocksize in Hessian of Lagrangianⓘ 100 Average blocksize in Hessian of Lagrangianⓘ 100.0 #Semicontinuitiesⓘ 0 #Nonlinear Semicontinuitiesⓘ 0 #SOS type 1ⓘ 0 #SOS type 2ⓘ 0 Infeasibility of initial pointⓘ 1e+04 Sparsity Jacobianⓘ Sparsity Hessian of Lagrangianⓘ

```\$offlisting
*
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          4        0        2        2        0        0        0        0
*
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        101        1        0      100        0        0        0        0
*  FX      0
*
*  Nonzero counts
*      Total    const       NL      DLL
*        401      301      100        0
*
*  Solve m using MINLP minimizing objvar;

Variables  i1,i2,i3,i4,i5,i6,i7,i8,i9,i10,i11,i12,i13,i14,i15,i16,i17,i18,i19
,i20,i21,i22,i23,i24,i25,i26,i27,i28,i29,i30,i31,i32,i33,i34,i35,i36
,i37,i38,i39,i40,i41,i42,i43,i44,i45,i46,i47,i48,i49,i50,i51,i52,i53
,i54,i55,i56,i57,i58,i59,i60,i61,i62,i63,i64,i65,i66,i67,i68,i69,i70
,i71,i72,i73,i74,i75,i76,i77,i78,i79,i80,i81,i82,i83,i84,i85,i86,i87
,i88,i89,i90,i91,i92,i93,i94,i95,i96,i97,i98,i99,i100,objvar;

Integer Variables  i1,i2,i3,i4,i5,i6,i7,i8,i9,i10,i11,i12,i13,i14,i15,i16,i17
,i18,i19,i20,i21,i22,i23,i24,i25,i26,i27,i28,i29,i30,i31,i32,i33,i34
,i35,i36,i37,i38,i39,i40,i41,i42,i43,i44,i45,i46,i47,i48,i49,i50,i51
,i52,i53,i54,i55,i56,i57,i58,i59,i60,i61,i62,i63,i64,i65,i66,i67,i68
,i69,i70,i71,i72,i73,i74,i75,i76,i77,i78,i79,i80,i81,i82,i83,i84,i85
,i86,i87,i88,i89,i90,i91,i92,i93,i94,i95,i96,i97,i98,i99,i100;

Equations  e1,e2,e3,e4;

e1.. 0.00841507*sqr(i1) + 0.0222536*sqr(i2) + 0.0056479*sqr(i3) + 0.00333322*
sqr(i4) + 0.00490963*sqr(i5) + 0.0221034*sqr(i6) + 0.00509899*sqr(i7) +
0.049464*sqr(i8) + 0.0171508*sqr(i9) + 0.0064643*sqr(i10) + 0.0218437*sqr(
i11) + 0.00346366*sqr(i12) + 0.0458502*sqr(i13) + 0.0747061*sqr(i14) +
0.0196511*sqr(i15) + 0.014222*sqr(i16) + 0.0147535*sqr(i17) + 0.00398615*
sqr(i18) + 0.00644484*sqr(i19) + 0.0322232*sqr(i20) + 0.00887889*sqr(i21)
+ 0.0434025*sqr(i22) + 0.00981376*sqr(i23) + 0.0133193*sqr(i24) +
0.00471036*sqr(i25) + 0.00359843*sqr(i26) + 0.0112312*sqr(i27) +
0.00476479*sqr(i28) + 0.00356255*sqr(i29) + 0.0730121*sqr(i30) +
0.00785721*sqr(i31) + 0.0243787*sqr(i32) + 0.0171188*sqr(i33) + 0.00439547
*sqr(i34) + 0.00502594*sqr(i35) + 0.0580619*sqr(i36) + 0.0135984*sqr(i37)
+ 0.00254137*sqr(i38) + 0.0153341*sqr(i39) + 0.109758*sqr(i40) +
0.0346065*sqr(i41) + 0.0127589*sqr(i42) + 0.011147*sqr(i43) + 0.0156318*
sqr(i44) + 0.00556588*sqr(i45) + 0.00302864*sqr(i46) + 0.0214898*sqr(i47)
+ 0.00499587*sqr(i48) + 0.00864393*sqr(i49) + 0.0228248*sqr(i50) +
0.0077726*sqr(i51) + 0.00992767*sqr(i52) + 0.0184506*sqr(i53) + 0.0113481*
sqr(i54) + 0.0067583*sqr(i55) + 0.0150416*sqr(i56) + 0.00324193*sqr(i57)
+ 0.00478196*sqr(i58) + 0.0132471*sqr(i59) + 0.00273446*sqr(i60) +
0.0282459*sqr(i61) + 0.0230221*sqr(i62) + 0.0240972*sqr(i63) + 0.00829946*
sqr(i64) + 0.00688665*sqr(i65) + 0.00858803*sqr(i66) + 0.00778038*sqr(i67)
+ 0.0082583*sqr(i68) + 0.022885*sqr(i69) + 0.00568332*sqr(i70) +
0.0234021*sqr(i71) + 0.00924249*sqr(i72) + 0.00669675*sqr(i73) + 0.0109501
*sqr(i74) + 0.00663385*sqr(i75) + 0.00328058*sqr(i76) + 0.0112814*sqr(i77)
+ 0.00341076*sqr(i78) + 0.0400653*sqr(i79) + 0.00876827*sqr(i80) +
0.0138276*sqr(i81) + 0.00246987*sqr(i82) + 0.0406516*sqr(i83) + 0.00947194
*sqr(i84) + 0.00647449*sqr(i85) + 0.0107715*sqr(i86) + 0.00803069*sqr(i87)
+ 0.106502*sqr(i88) + 0.00815263*sqr(i89) + 0.0171707*sqr(i90) +
0.0163522*sqr(i91) + 0.00911726*sqr(i92) + 0.00287317*sqr(i93) +
0.00360309*sqr(i94) + 0.00699161*sqr(i95) + 0.0340959*sqr(i96) +
0.00958446*sqr(i97) + 0.0147951*sqr(i98) + 0.0177595*sqr(i99) + 0.0208523*
sqr(i100) + 0.00692522*i1*i2 + 0.00066464*i1*i3 + 0.00388744*i1*i4 +
0.001108218*i1*i5 + 0.0046712*i1*i6 + 0.00771824*i1*i7 + 0.0020653*i1*i8
+ 0.001524626*i1*i9 + 0.00484724*i1*i10 + 0.00733242*i1*i11 + 0.00556218*
i1*i12 + 0.0052571*i1*i13 + 0.0218926*i1*i14 + 0.01352862*i1*i15 +
0.00549784*i1*i16 + 0.00235342*i1*i17 + 0.00448206*i1*i18 + 0.0072148*i1*
i19 + 0.00958894*i1*i20 + 0.00376328*i1*i21 + 0.0117501*i1*i22 +
0.00575998*i1*i23 - 0.000109147*i1*i24 + 0.000604944*i1*i25 + 0.00473296*
i1*i26 + 0.000356572*i1*i27 - 0.001552262*i1*i28 + 0.00119092*i1*i29 +
0.01373684*i1*i30 + 0.0059113*i1*i31 + 0.00623524*i1*i32 + 0.00801204*i1*
i33 + 0.00108736*i1*i34 + 0.001491474*i1*i35 + 0.01080356*i1*i36 +
0.00559202*i1*i37 + 7.8057e-6*i1*i38 + 0.00831004*i1*i39 + 0.001096208*i1*
i40 + 0.001136658*i1*i41 + 0.0073715*i1*i42 + 0.000726938*i1*i43 +
0.00621872*i1*i44 + 0.00646596*i1*i45 + 0.00441466*i1*i46 + 0.001262528*i1
*i47 + 0.00567366*i1*i48 + 0.00690472*i1*i49 + 0.01140754*i1*i50 +
0.00275514*i1*i51 + 0.00633434*i1*i52 + 0.00842252*i1*i53 + 0.00674544*i1*
i54 + 0.00577156*i1*i55 + 0.000723972*i1*i56 + 0.00617654*i1*i57 +
0.00426758*i1*i58 + 0.00581362*i1*i59 + 0.00305964*i1*i60 + 0.00915838*i1*
i61 + 0.00408204*i1*i62 + 0.00526036*i1*i63 + 0.00641708*i1*i64 +
0.001311362*i1*i65 + 0.00589896*i1*i66 + 0.001450664*i1*i67 + 0.0054669*i1
*i68 + 0.00759698*i1*i69 + 0.0069591*i1*i70 + 0.0023689*i1*i71 + 0.0026146
*i1*i72 + 0.00520422*i1*i73 + 0.00959956*i1*i74 + 0.00799166*i1*i75 +
0.00256248*i1*i76 + 0.01210352*i1*i77 + 0.00469514*i1*i78 + 0.00329676*i1*
i79 + 0.0068214*i1*i80 + 0.00190637*i1*i81 + 0.00256972*i1*i82 -
0.00577696*i1*i83 + 0.00245394*i1*i84 + 0.00585966*i1*i85 + 0.00330078*i1*
i86 + 0.00362852*i1*i87 + 0.0064137*i1*i88 + 0.00375038*i1*i89 +
0.00666048*i1*i90 + 0.00942176*i1*i91 + 0.00379828*i1*i92 + 0.00246526*i1*
i93 + 0.0029997*i1*i94 + 0.00592606*i1*i95 + 0.0136565*i1*i96 + 0.00562112
*i1*i97 + 0.0031101*i1*i98 + 0.00328418*i1*i99 + 0.00992138*i1*i100 +
0.01159836*i2*i3 + 0.00432612*i2*i4 + 0.01055774*i2*i5 + 0.0235592*i2*i6
+ 0.0053913*i2*i7 + 0.01748966*i2*i8 + 0.01322526*i2*i9 + 0.01103896*i2*
i10 + 0.001420928*i2*i11 + 0.00303766*i2*i12 + 0.0325414*i2*i13 +
0.0528886*i2*i14 + 0.0344486*i2*i15 + 0.01889664*i2*i16 + 0.01085498*i2*
i17 + 0.01133696*i2*i18 + 0.0105108*i2*i19 + 0.041965*i2*i20 + 0.01908526*
i2*i21 + 0.0438608*i2*i22 + 0.01760436*i2*i23 + 0.0177692*i2*i24 +
0.01401386*i2*i25 + 0.01130076*i2*i26 + 0.0201926*i2*i27 + 0.00893526*i2*
i28 + 0.01013464*i2*i29 + 0.0522552*i2*i30 + 0.00674062*i2*i31 + 0.0386894
*i2*i32 + 0.01840562*i2*i33 + 0.0079061*i2*i34 + 0.01050574*i2*i35 +
0.038882*i2*i36 + 0.0209782*i2*i37 + 0.00569346*i2*i38 + 0.0259324*i2*i39
+ 0.0472088*i2*i40 + 0.0282636*i2*i41 + 0.0225892*i2*i42 + 0.01104052*i2*
i43 + 0.0218496*i2*i44 + 0.00682534*i2*i45 + 0.01022898*i2*i46 + 0.0273094
*i2*i47 + 0.01045064*i2*i48 + 0.01767338*i2*i49 + 0.0311902*i2*i50 +
0.0126455*i2*i51 + 0.0206168*i2*i52 + 0.0261894*i2*i53 + 0.024527*i2*i54
+ 0.01734138*i2*i55 + 0.01224052*i2*i56 + 0.01152072*i2*i57 + 0.01028864*
i2*i58 + 0.01883544*i2*i59 + 0.00908648*i2*i60 + 0.0449708*i2*i61 +
0.0363664*i2*i62 + 0.01577062*i2*i63 + 0.01266282*i2*i64 + 0.01385216*i2*
i65 + 0.00440902*i2*i66 + 0.01711764*i2*i67 + 0.0110787*i2*i68 + 0.0341778
*i2*i69 + 0.0156542*i2*i70 + 0.01891112*i2*i71 + 0.0216326*i2*i72 +
0.01534328*i2*i73 + 0.01661334*i2*i74 + 0.01534594*i2*i75 + 0.01116732*i2*
i76 + 0.01402982*i2*i77 + 0.00963242*i2*i78 + 0.0200668*i2*i79 +
0.01379116*i2*i80 + 0.01910046*i2*i81 + 0.0077605*i2*i82 - 0.000954558*i2*
i83 + 0.01255918*i2*i84 + 0.0126639*i2*i85 + 0.0201936*i2*i86 + 0.017931*
i2*i87 + 0.0389418*i2*i88 + 0.00845916*i2*i89 + 0.0267914*i2*i90 +
0.0193905*i2*i91 + 0.01261014*i2*i92 + 0.0069012*i2*i93 + 0.00876014*i2*
i94 + 0.01829908*i2*i95 + 0.0373396*i2*i96 + 0.0211262*i2*i97 + 0.01549032
*i2*i98 + 0.0247114*i2*i99 + 0.0324248*i2*i100 - 0.000720538*i3*i4 +
0.00453322*i3*i5 + 0.00638226*i3*i6 + 0.000938158*i3*i7 + 0.0035154*i3*i8
+ 0.00681962*i3*i9 + 0.006345*i3*i10 + 0.00232904*i3*i11 - 0.00054599*i3*
i12 + 0.01850556*i3*i13 + 0.01892336*i3*i14 + 0.00820906*i3*i15 +
0.00848796*i3*i16 + 0.0100743*i3*i17 + 0.00327798*i3*i18 + 0.000498452*i3*
i19 + 0.01775572*i3*i20 + 0.00919688*i3*i21 + 0.01282772*i3*i22 +
0.00853066*i3*i23 + 0.00506148*i3*i24 + 0.004557*i3*i25 + 0.001737768*i3*
i26 + 0.00560326*i3*i27 + 0.00374962*i3*i28 + 0.000427408*i3*i29 +
0.01831098*i3*i30 + 0.00791496*i3*i31 + 0.01306*i3*i32 + 0.0143109*i3*i33
+ 0.00324578*i3*i34 + 0.00289704*i3*i35 + 0.01899172*i3*i36 + 0.00855898*
i3*i37 + 0.000764782*i3*i38 + 0.01045622*i3*i39 + 0.0241684*i3*i40 +
0.01022702*i3*i41 + 0.0096569*i3*i42 + 0.00605256*i3*i43 + 0.0087656*i3*
i44 + 0.00231868*i3*i45 + 0.003075*i3*i46 + 0.00904418*i3*i47 + 0.00346386
*i3*i48 + 0.00970054*i3*i49 + 0.0107517*i3*i50 + 0.00833706*i3*i51 +
0.00601022*i3*i52 + 0.00885472*i3*i53 + 0.0087269*i3*i54 + 0.00799796*i3*
i55 + 0.0077742*i3*i56 + 0.00233028*i3*i57 + 0.00392772*i3*i58 +
0.00960436*i3*i59 + 0.000506858*i3*i60 + 0.01485036*i3*i61 + 0.01172454*i3
*i62 + 0.00763564*i3*i63 + 0.00510368*i3*i64 + 0.00739458*i3*i65 +
0.00321864*i3*i66 + 0.00506992*i3*i67 + 0.001582392*i3*i68 + 0.0133327*i3*
i69 + 0.00346984*i3*i70 + 0.00591914*i3*i71 + 0.0050918*i3*i72 +
0.00762942*i3*i73 + 0.0072567*i3*i74 + 0.0028432*i3*i75 + 0.00258746*i3*
i76 + 0.00665946*i3*i77 + 0.001559716*i3*i78 + 0.0114221*i3*i79 +
0.00359546*i3*i80 + 0.00675946*i3*i81 + 0.001328782*i3*i82 + 0.00450512*i3
*i83 + 0.00859628*i3*i84 + 0.00541618*i3*i85 + 0.01126372*i3*i86 +
0.00604642*i3*i87 + 0.01802074*i3*i88 + 0.0056414*i3*i89 + 0.00952436*i3*
i90 + 0.00568388*i3*i91 + 0.0086732*i3*i92 + 0.001482822*i3*i93 +
0.0026677*i3*i94 + 0.00675394*i3*i95 + 0.01169216*i3*i96 + 0.0076724*i3*
i97 + 0.00761804*i3*i98 + 0.01192344*i3*i99 + 0.01326866*i3*i100 +
0.00169903*i4*i5 + 0.00300136*i4*i6 + 0.00385392*i4*i7 + 0.00382362*i4*i8
+ 0.00575034*i4*i9 + 0.00125203*i4*i10 + 0.000828078*i4*i11 + 0.00404896*
i4*i12 - 0.001180878*i4*i13 + 0.00956206*i4*i14 + 0.00571904*i4*i15 +
0.0047927*i4*i16 + 0.001736122*i4*i17 + 0.001900434*i4*i18 + 0.00498296*i4
*i19 + 0.0055112*i4*i20 + 0.00199047*i4*i21 + 0.00302926*i4*i22 +
0.001107052*i4*i23 + 0.0032099*i4*i24 + 0.00202704*i4*i25 + 0.0049441*i4*
i26 + 0.00296714*i4*i27 + 0.001430786*i4*i28 + 0.00335542*i4*i29 +
0.0072271*i4*i30 + 0.001983328*i4*i31 + 0.00263338*i4*i32 + 0.0034098*i4*
i33 + 0.001978102*i4*i34 + 0.00248436*i4*i35 + 0.001037234*i4*i36 +
0.001931824*i4*i37 + 0.00154955*i4*i38 + 0.00293776*i4*i39 - 0.01282698*i4
*i40 + 0.001937926*i4*i41 + 0.0052959*i4*i42 + 0.001856036*i4*i43 +
0.000740384*i4*i44 + 0.00372246*i4*i45 + 0.00362974*i4*i46 + 0.001687258*
i4*i47 + 0.00297792*i4*i48 + 0.0024381*i4*i49 + 0.00581304*i4*i50 +
0.000775592*i4*i51 + 0.00512872*i4*i52 + 0.00302932*i4*i53 + 0.00451004*i4
*i54 + 0.00355054*i4*i55 + 0.000365898*i4*i56 + 0.00396452*i4*i57 +
0.00218522*i4*i58 + 0.001602712*i4*i59 + 0.00378946*i4*i60 + 0.00528342*i4
*i61 + 0.00345546*i4*i62 + 0.0072364*i4*i63 + 0.00460504*i4*i64 +
0.00362066*i4*i65 + 0.00176825*i4*i66 + 0.00326082*i4*i67 + 0.00494324*i4*
i68 + 0.00478058*i4*i69 + 0.0047424*i4*i70 + 0.00406804*i4*i71 +
0.00356438*i4*i72 + 0.0039191*i4*i73 + 0.00506266*i4*i74 + 0.005213*i4*i75
+ 0.00334114*i4*i76 + 0.00410168*i4*i77 + 0.00325268*i4*i78 + 0.000621396
*i4*i79 + 0.00679868*i4*i80 + 0.001665408*i4*i81 + 0.00231708*i4*i82 -
0.0025243*i4*i83 + 0.00277762*i4*i84 + 0.0040202*i4*i85 + 0.001500566*i4*
i86 + 0.001680814*i4*i87 + 0.00640404*i4*i88 + 0.00397656*i4*i89 +
0.000508164*i4*i90 + 0.00565534*i4*i91 + 0.0031999*i4*i92 + 0.0007233*i4*
i93 + 0.001347788*i4*i94 + 0.00386662*i4*i95 + 0.0056032*i4*i96 +
0.00392786*i4*i97 + 0.0032706*i4*i98 + 0.000716722*i4*i99 + 0.00200998*i4*
i100 + 0.00725878*i5*i6 + 0.000634496*i5*i7 + 0.0112129*i5*i8 + 0.006535*
i5*i9 + 0.0076756*i5*i10 - 0.00455426*i5*i11 + 0.001111236*i5*i12 +
0.01473142*i5*i13 + 0.01556352*i5*i14 + 0.00889148*i5*i15 + 0.00833956*i5*
i16 + 0.01155304*i5*i17 + 0.0044319*i5*i18 + 0.0061696*i5*i19 + 0.01660846
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i10*i65 + 0.00671784*i10*i66 + 0.00876736*i10*i67 + 0.00330284*i10*i68 +
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i10*i79 + 0.00722624*i10*i80 + 0.00973154*i10*i81 + 0.00371556*i10*i82 +
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0.0124516*i10*i90 + 0.00915752*i10*i91 + 0.00913708*i10*i92 + 0.00200378*
i10*i93 + 0.00536928*i10*i94 + 0.00823672*i10*i95 + 0.01736144*i10*i96 +
0.01105742*i10*i97 + 0.01023842*i10*i98 + 0.01685104*i10*i99 + 0.01457986*
i10*i100 + 0.000833086*i11*i12 + 0.00999478*i11*i13 + 0.01344484*i11*i14
+ 0.0031808*i11*i15 + 0.01117228*i11*i16 + 0.000697152*i11*i17 +
0.000585828*i11*i18 + 0.00585952*i11*i19 + 0.00859976*i11*i20 + 0.00502902
*i11*i21 + 0.00447154*i11*i22 + 0.001969568*i11*i23 + 0.0049358*i11*i24 -
0.00029705*i11*i25 + 0.0008833*i11*i26 + 0.00788936*i11*i27 + 0.00223564*
i11*i28 - 0.001370818*i11*i29 + 0.0148367*i11*i30 + 0.01084338*i11*i31 +
0.000606756*i11*i32 + 0.00591896*i11*i33 - 0.00408456*i11*i34 - 0.002724*
i11*i35 + 0.01495302*i11*i36 + 0.0001528802*i11*i37 + 0.000200858*i11*i38
+ 0.00843216*i11*i39 + 0.01341476*i11*i40 + 0.01160686*i11*i41 +
0.00464728*i11*i42 + 0.00803576*i11*i43 + 0.00270742*i11*i44 - 0.00352162*
i11*i45 + 0.000947796*i11*i46 + 0.00388898*i11*i47 + 0.00557236*i11*i48 +
0.00208008*i11*i49 + 0.000931698*i11*i50 + 0.000654446*i11*i51 +
0.00650504*i11*i52 + 0.000501194*i11*i53 + 0.00681518*i11*i54 + 0.00601122
*i11*i55 - 0.00507122*i11*i56 + 0.000483176*i11*i57 + 0.00482018*i11*i58
+ 0.0064067*i11*i59 - 0.000166498*i11*i60 + 0.00575774*i11*i61 +
0.00725456*i11*i62 + 0.00219412*i11*i63 + 0.0084673*i11*i64 + 0.000333436*
i11*i65 + 0.00655332*i11*i66 - 0.00257168*i11*i67 + 0.01199786*i11*i68 +
0.0059299*i11*i69 + 0.001843394*i11*i70 + 0.01060724*i11*i71 + 0.00647206*
i11*i72 + 0.00231676*i11*i73 + 0.00580344*i11*i74 + 0.00620538*i11*i75 -
0.000334258*i11*i76 + 0.00656424*i11*i77 - 0.001286316*i11*i78 +
0.00546106*i11*i79 - 0.000202642*i11*i80 + 0.00426114*i11*i81 - 0.00204892
*i11*i82 + 0.01117602*i11*i83 + 0.01034244*i11*i84 + 0.00449542*i11*i85 +
0.00797378*i11*i86 - 0.000792844*i11*i87 + 0.01939124*i11*i88 + 0.00432784
*i11*i89 + 0.00204578*i11*i90 + 0.021152*i11*i91 + 0.00283286*i11*i92 -
0.00407532*i11*i93 - 0.001198622*i11*i94 + 0.0056114*i11*i95 + 0.00560696*
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0.01396562*i41*i91 + 0.01458222*i41*i92 + 0.0072903*i41*i93 + 0.00709746*
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0.00934936*i42*i75 + 0.00505832*i42*i76 + 0.01458566*i42*i77 + 0.00728638*
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0.00313858*i43*i60 + 0.01509816*i43*i61 + 0.0162044*i43*i62 + 0.01875628*
i43*i63 + 0.01240346*i43*i64 + 0.0085184*i43*i65 + 0.0097536*i43*i66 +
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i43*i70 + 0.01833662*i43*i71 + 0.01219044*i43*i72 + 0.00997222*i43*i73 +
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i43*i84 + 0.0073079*i43*i85 + 0.01024086*i43*i86 + 0.00333288*i43*i87 +
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i43*i91 + 0.00897022*i43*i92 + 0.00315402*i43*i93 + 0.00504118*i43*i94 +
0.01075858*i43*i95 + 0.00678594*i43*i96 + 0.01260626*i43*i97 + 0.0163881*
i43*i98 + 0.01009846*i43*i99 + 0.01154306*i43*i100 + 0.00483446*i44*i45 +
0.00652268*i44*i46 + 0.0242272*i44*i47 + 0.00478826*i44*i48 + 0.01685648*
i44*i49 + 0.020425*i44*i50 + 0.00923526*i44*i51 + 0.01214276*i44*i52 +
0.01807778*i44*i53 + 0.01714928*i44*i54 + 0.0117815*i44*i55 + 0.01675568*
i44*i56 + 0.0065756*i44*i57 + 0.01226174*i44*i58 + 0.0107529*i44*i59 +
0.00316098*i44*i60 + 0.0237412*i44*i61 + 0.023095*i44*i62 + 0.0261176*i44*
i63 + 0.01217274*i44*i64 + 0.01008618*i44*i65 + 0.0100818*i44*i66 +
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i44*i70 + 0.0238346*i44*i71 + 0.01469328*i44*i72 + 0.01153818*i44*i73 +
0.0107527*i44*i74 + 0.00664436*i44*i75 + 0.00643936*i44*i76 + 0.01819866*
i44*i77 + 0.00401038*i44*i78 + 0.00860378*i44*i79 + 0.01052694*i44*i80 +
0.01791956*i44*i81 + 0.001302356*i44*i82 + 0.024415*i44*i83 + 0.01318656*
i44*i84 + 0.00691488*i44*i85 + 0.0134211*i44*i86 + 0.01005166*i44*i87 +
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0.01196692*i44*i95 + 0.01664976*i44*i96 + 0.01462126*i44*i97 + 0.0157382*
i44*i98 + 0.01533824*i44*i99 + 0.0188597*i44*i100 + 0.00317774*i45*i46 +
0.00420624*i45*i47 + 0.00199361*i45*i48 + 0.0050265*i45*i49 + 0.00894044*
i45*i50 + 0.00284776*i45*i51 + 0.00547162*i45*i52 + 0.00269966*i45*i53 +
0.0064379*i45*i54 + 0.00472118*i45*i55 + 0.0042126*i45*i56 + 0.00394074*
i45*i57 + 0.00265196*i45*i58 + 0.00448504*i45*i59 + 0.001797504*i45*i60 +
0.00867806*i45*i61 + 0.00322858*i45*i62 + 0.00607352*i45*i63 + 0.00436738*
i45*i64 + 0.00237578*i45*i65 + 0.0044976*i45*i66 + 0.00181419*i45*i67 +
0.00495262*i45*i68 + 0.00570214*i45*i69 + 0.00422674*i45*i70 + 0.001748284
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0.0046385*i45*i75 + 0.001228842*i45*i76 + 0.00595824*i45*i77 + 0.0027183*
i45*i78 + 0.00108409*i45*i79 + 0.00761658*i45*i80 + 0.0005468*i45*i81 +
0.001647768*i45*i82 - 0.00572218*i45*i83 + 0.00291394*i45*i84 + 0.00667112
*i45*i85 + 0.00283124*i45*i86 + 0.00214236*i45*i87 + 0.00913532*i45*i88 +
0.0031579*i45*i89 + 0.001671266*i45*i90 + 0.007457*i45*i91 + 0.00539294*
i45*i92 + 0.001548892*i45*i93 + 0.00325768*i45*i94 + 0.00415906*i45*i95 +
0.00472416*i45*i96 + 0.00257908*i45*i97 + 0.00311904*i45*i98 - 0.00028754*
i45*i99 + 0.00641254*i45*i100 + 0.00936266*i46*i47 + 0.00551424*i46*i48 +
0.00665328*i46*i49 + 0.01254298*i46*i50 + 0.00457552*i46*i51 + 0.00723508*
i46*i52 + 0.01013924*i46*i53 + 0.00835722*i46*i54 + 0.00612552*i46*i55 +
0.00568528*i46*i56 + 0.00506602*i46*i57 + 0.00547684*i46*i58 + 0.00630834*
i46*i59 + 0.0034076*i46*i60 + 0.01269782*i46*i61 + 0.01056202*i46*i62 +
0.00905674*i46*i63 + 0.00727642*i46*i64 + 0.0053986*i46*i65 + 0.00499194*
i46*i66 + 0.00693256*i46*i67 + 0.00384534*i46*i68 + 0.01113952*i46*i69 +
0.00571676*i46*i70 + 0.00918194*i46*i71 + 0.00582038*i46*i72 + 0.00587208*
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i46*i80 + 0.00786638*i46*i81 + 0.001854684*i46*i82 + 0.00407872*i46*i83 +
0.00621788*i46*i84 + 0.00606418*i46*i85 + 0.00669516*i46*i86 + 0.00483036*
i46*i87 + 0.00889994*i46*i88 + 0.00341184*i46*i89 + 0.00883678*i46*i90 +
0.00699852*i46*i91 + 0.00577214*i46*i92 + 0.00238288*i46*i93 + 0.001681122
*i46*i94 + 0.00660328*i46*i95 + 0.0125098*i46*i96 + 0.00829924*i46*i97 +
0.00843732*i46*i98 + 0.00930502*i46*i99 + 0.01141018*i46*i100 + 0.00622806
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0.0096102*i47*i59 + 0.00476024*i47*i60 + 0.0291008*i47*i61 + 0.0293252*i47
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0.01074494*i47*i66 + 0.01192482*i47*i67 + 0.0072756*i47*i68 + 0.0259978*
i47*i69 + 0.01196354*i47*i70 + 0.0346772*i47*i71 + 0.01997802*i47*i72 +
0.0109755*i47*i73 + 0.01126216*i47*i74 + 0.00543986*i47*i75 + 0.00507998*
i47*i76 + 0.01031016*i47*i77 + 0.0051788*i47*i78 + 0.001275304*i47*i79 +
0.00993436*i47*i80 + 0.0302174*i47*i81 + 0.0025327*i47*i82 + 0.0227778*i47
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0.00789154*i47*i87 + 0.0151434*i47*i88 + 0.001278866*i47*i89 + 0.0158996*
i47*i90 + 0.01154264*i47*i91 + 0.01393698*i47*i92 + 0.00304714*i47*i93 +
0.00512466*i47*i94 + 0.01429612*i47*i95 + 0.01681572*i47*i96 + 0.01931984*
i47*i97 + 0.0267484*i47*i98 + 0.01797768*i47*i99 + 0.0282598*i47*i100 +
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0.0392412*i62*i69 + 0.01609634*i62*i70 + 0.0216048*i62*i71 + 0.0216526*i62
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0.00779326*i62*i76 + 0.01429558*i62*i77 + 0.0081994*i62*i78 + 0.024889*i62
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0.01114552*i62*i83 + 0.01793036*i62*i84 + 0.01444614*i62*i85 + 0.01879448*
i62*i86 + 0.01466504*i62*i87 + 0.0326604*i62*i88 + 0.01169144*i62*i89 +
0.0254028*i62*i90 + 0.01965996*i62*i91 + 0.01132102*i62*i92 + 0.0046546*
i62*i93 + 0.00635342*i62*i94 + 0.0209304*i62*i95 + 0.040751*i62*i96 +
0.0251822*i62*i97 + 0.0238578*i62*i98 + 0.0225858*i62*i99 + 0.0313134*i62*
i100 + 0.01545704*i63*i64 + 0.01086358*i63*i65 + 0.00996396*i63*i66 +
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0.01790944*i63*i81 + 0.001490592*i63*i82 + 0.0267338*i63*i83 + 0.01586496*
i63*i84 + 0.01166282*i63*i85 + 0.01568614*i63*i86 + 0.00753188*i63*i87 +
0.0417782*i63*i88 + 0.0112216*i63*i89 + 0.00371206*i63*i90 + 0.01829192*
i63*i91 + 0.01841964*i63*i92 + 0.00206622*i63*i93 + 0.00505172*i63*i94 +
0.01487174*i63*i95 + 0.01414348*i63*i96 + 0.0156802*i63*i97 + 0.01823426*
i63*i98 + 0.01258764*i63*i99 + 0.01994098*i63*i100 + 0.00854654*i64*i65 +
0.01079866*i64*i66 + 0.00602732*i64*i67 + 0.00921276*i64*i68 + 0.01464414*
i64*i69 + 0.00664932*i64*i70 + 0.0144736*i64*i71 + 0.00978338*i64*i72 +
0.00959208*i64*i73 + 0.0112566*i64*i74 + 0.00671142*i64*i75 + 0.00408206*
i64*i76 + 0.01167568*i64*i77 + 0.00375274*i64*i78 + 0.00404336*i64*i79 +
0.00963238*i64*i80 + 0.0122908*i64*i81 + 0.001806772*i64*i82 + 0.01577266*
i64*i83 + 0.01128074*i64*i84 + 0.0095111*i64*i85 + 0.0097723*i64*i86 +
0.00346618*i64*i87 + 0.01289324*i64*i88 + 0.00453186*i64*i89 + 0.0078486*
i64*i90 + 0.01310134*i64*i91 + 0.00985686*i64*i92 + 0.00257788*i64*i93 +
0.00260324*i64*i94 + 0.0108877*i64*i95 + 0.01349616*i64*i96 + 0.01306042*
i64*i97 + 0.01405114*i64*i98 + 0.0115142*i64*i99 + 0.01728302*i64*i100 +
0.0048225*i65*i66 + 0.00871696*i65*i67 + 0.00504014*i65*i68 + 0.01673796*
i65*i69 + 0.00728674*i65*i70 + 0.00969202*i65*i71 + 0.0082057*i65*i72 +
0.0103704*i65*i73 + 0.00998004*i65*i74 + 0.00672722*i65*i75 + 0.00633346*
i65*i76 + 0.00774852*i65*i77 + 0.00440922*i65*i78 + 0.01343946*i65*i79 +
0.00798994*i65*i80 + 0.01225132*i65*i81 + 0.00444398*i65*i82 + 0.00673302*
i65*i83 + 0.0109598*i65*i84 + 0.00683186*i65*i85 + 0.01183874*i65*i86 +
0.0090907*i65*i87 + 0.0283952*i65*i88 + 0.00785096*i65*i89 + 0.01125058*
i65*i90 + 0.00510526*i65*i91 + 0.00837574*i65*i92 + 0.00385798*i65*i93 +
0.00464904*i65*i94 + 0.00896456*i65*i95 + 0.0160694*i65*i96 + 0.0113557*
i65*i97 + 0.01155766*i65*i98 + 0.01443876*i65*i99 + 0.01238186*i65*i100 +
0.00548536*i66*i67 + 0.00630564*i66*i68 + 0.00939978*i66*i69 + 0.00431468*
i66*i70 + 0.01542742*i66*i71 + 0.0071665*i66*i72 + 0.00755022*i66*i73 +
0.00838922*i66*i74 + 0.00386922*i66*i75 + 0.001951058*i66*i76 + 0.01146338
*i66*i77 + 0.001980078*i66*i78 + 0.00444902*i66*i79 + 0.00356762*i66*i80
+ 0.00956806*i66*i81 - 0.00023183*i66*i82 + 0.01703884*i66*i83 +
0.01002452*i66*i84 + 0.0062546*i66*i85 + 0.00563304*i66*i86 + 0.00514984*
i66*i87 + 0.01908326*i66*i88 + 0.00457928*i66*i89 + 0.003995*i66*i90 +
0.0080501*i66*i91 + 0.00810108*i66*i92 + 0.00328186*i66*i93 + 0.00369064*
i66*i94 + 0.0058103*i66*i95 + 0.00438208*i66*i96 + 0.00867896*i66*i97 +
0.0114927*i66*i98 + 0.01103938*i66*i99 + 0.00981454*i66*i100 + 0.00310364*
i67*i68 + 0.0195756*i67*i69 + 0.00833924*i67*i70 + 0.01122*i67*i71 +
0.00862168*i67*i72 + 0.00711248*i67*i73 + 0.00958304*i67*i74 + 0.00671208*
i67*i75 + 0.00667666*i67*i76 + 0.00639998*i67*i77 + 0.00746068*i67*i78 +
0.0164696*i67*i79 + 0.00952472*i67*i80 + 0.01054908*i67*i81 + 0.00295206*
i67*i82 + 0.00786538*i67*i83 + 0.00812566*i67*i84 + 0.00774908*i67*i85 +
0.01084866*i67*i86 + 0.01179554*i67*i87 + 0.022894*i67*i88 + 0.00619526*
i67*i89 + 0.01517056*i67*i90 + 0.00567344*i67*i91 + 0.00901318*i67*i92 +
0.00388018*i67*i93 + 0.0036956*i67*i94 + 0.008896*i67*i95 + 0.021896*i67*
i96 + 0.01327636*i67*i97 + 0.0109*i67*i98 + 0.0178563*i67*i99 + 0.01328366
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+ 0.01077146*i68*i72 + 0.00701056*i68*i73 + 0.00764336*i68*i74 +
0.01085638*i68*i75 + 0.00267198*i68*i76 + 0.00622086*i68*i77 + 0.0026961*
i68*i78 + 0.01283914*i68*i79 + 0.00651186*i68*i80 + 0.00444824*i68*i81 +
0.00245108*i68*i82 - 0.000724804*i68*i83 + 0.01001432*i68*i84 + 0.00659112
*i68*i85 + 0.00798872*i68*i86 + 0.00378278*i68*i87 + 0.0249894*i68*i88 +
0.00935338*i68*i89 + 0.00406214*i68*i90 + 0.01547864*i68*i91 + 0.0026383*
i68*i92 + 0.001956366*i68*i93 + 0.00433104*i68*i94 + 0.0086862*i68*i95 +
0.00871594*i68*i96 + 0.00917804*i68*i97 + 0.01147728*i68*i98 + 0.000904318
*i68*i99 + 0.0095902*i68*i100 + 0.01716134*i69*i70 + 0.0210128*i69*i71 +
0.01970512*i69*i72 + 0.01824406*i69*i73 + 0.0202038*i69*i74 + 0.0166321*
i69*i75 + 0.0080034*i69*i76 + 0.01785698*i69*i77 + 0.00956708*i69*i78 +
0.0273938*i69*i79 + 0.01578286*i69*i80 + 0.01986548*i69*i81 + 0.00472512*
i69*i82 + 0.0064477*i69*i83 + 0.0205866*i69*i84 + 0.01485404*i69*i85 +
0.0219926*i69*i86 + 0.01726592*i69*i87 + 0.044296*i69*i88 + 0.01519388*i69
*i89 + 0.0245318*i69*i90 + 0.019668*i69*i91 + 0.01322886*i69*i92 +
0.00622812*i69*i93 + 0.00886068*i69*i94 + 0.0207946*i69*i95 + 0.0369544*
i69*i96 + 0.0252064*i69*i97 + 0.0246794*i69*i98 + 0.0240826*i69*i99 +
0.0322226*i69*i100 + 0.01122678*i70*i71 + 0.00985708*i70*i72 + 0.00817346*
i70*i73 + 0.01042594*i70*i74 + 0.0087512*i70*i75 + 0.00587552*i70*i76 +
0.00956692*i70*i77 + 0.00604702*i70*i78 + 0.01012786*i70*i79 + 0.00894572*
i70*i80 + 0.00937532*i70*i81 + 0.0040741*i70*i82 + 0.001290572*i70*i83 +
0.00820512*i70*i84 + 0.00683756*i70*i85 + 0.00768078*i70*i86 + 0.00827048*
i70*i87 + 0.01990564*i70*i88 + 0.007123*i70*i89 + 0.00998564*i70*i90 +
0.00953688*i70*i91 + 0.00558782*i70*i92 + 0.00342686*i70*i93 + 0.00568486*
i70*i94 + 0.00914938*i70*i95 + 0.01630104*i70*i96 + 0.01110616*i70*i97 +
0.010247*i70*i98 + 0.00833958*i70*i99 + 0.01265252*i70*i100 + 0.0220254*
i71*i72 + 0.0095213*i71*i73 + 0.01209936*i71*i74 + 0.00527094*i71*i75 +
0.00557218*i71*i76 + 0.01262004*i71*i77 + 0.0037353*i71*i78 - 0.000223588*
i71*i79 + 0.00801532*i71*i80 + 0.0286786*i71*i81 + 0.000788336*i71*i82 +
0.0387752*i71*i83 + 0.01552284*i71*i84 + 0.00720994*i71*i85 + 0.01148132*
i71*i86 + 0.00870698*i71*i87 + 0.028675*i71*i88 + 0.00544718*i71*i89 +
0.00673884*i71*i90 + 0.01008984*i71*i91 + 0.01241834*i71*i92 + 0.0025495*
i71*i93 + 0.00280272*i71*i94 + 0.00947552*i71*i95 + 0.0070495*i71*i96 +
0.0170916*i71*i97 + 0.0269036*i71*i98 + 0.01506306*i71*i99 + 0.0206782*i71
*i100 + 0.00925426*i72*i73 + 0.00967792*i72*i74 + 0.00847338*i72*i75 +
0.005213*i72*i76 + 0.00908662*i72*i77 + 0.00316872*i72*i78 + 0.00898138*
i72*i79 + 0.0069179*i72*i80 + 0.0151281*i72*i81 + 0.00348424*i72*i82 +
0.01111986*i72*i83 + 0.01165966*i72*i84 + 0.0064802*i72*i85 + 0.00959246*
i72*i86 + 0.0084611*i72*i87 + 0.0240956*i72*i88 + 0.00687054*i72*i89 +
0.0094553*i72*i90 + 0.0110757*i72*i91 + 0.00543508*i72*i92 + 0.0037306*i72
*i93 + 0.00500972*i72*i94 + 0.01005818*i72*i95 + 0.01294332*i72*i96 +
0.01344022*i72*i97 + 0.01593132*i72*i98 + 0.0093216*i72*i99 + 0.01640118*
i72*i100 + 0.01198598*i73*i74 + 0.00750544*i73*i75 + 0.0050216*i73*i76 +
0.01285904*i73*i77 + 0.00339452*i73*i78 + 0.00891788*i73*i79 + 0.00948614*
i73*i80 + 0.00944098*i73*i81 + 0.00409826*i73*i82 + 0.00488372*i73*i83 +
0.01210326*i73*i84 + 0.00827726*i73*i85 + 0.0117403*i73*i86 + 0.00812428*
i73*i87 + 0.031499*i73*i88 + 0.00909586*i73*i89 + 0.00829156*i73*i90 +
0.0112196*i73*i91 + 0.00781298*i73*i92 + 0.00380884*i73*i93 + 0.00624296*
i73*i94 + 0.01005016*i73*i95 + 0.01437472*i73*i96 + 0.011277*i73*i97 +
0.01058622*i73*i98 + 0.0121454*i73*i99 + 0.01373088*i73*i100 + 0.01080198*
i74*i75 + 0.00656182*i74*i76 + 0.01437682*i74*i77 + 0.00746976*i74*i78 +
0.0158128*i74*i79 + 0.01161714*i74*i80 + 0.01098286*i74*i81 + 0.00409892*
i74*i82 + 0.00263806*i74*i83 + 0.01368742*i74*i84 + 0.00966578*i74*i85 +
0.0126469*i74*i86 + 0.0097362*i74*i87 + 0.0236752*i74*i88 + 0.0087263*i74*
i89 + 0.01653132*i74*i90 + 0.01259886*i74*i91 + 0.0074886*i74*i92 +
0.00612882*i74*i93 + 0.00553384*i74*i94 + 0.01256076*i74*i95 + 0.022837*
i74*i96 + 0.01489052*i74*i97 + 0.0138654*i74*i98 + 0.01608016*i74*i99 +
0.0185439*i74*i100 + 0.00483222*i75*i76 + 0.0084646*i75*i77 + 0.00605234*
i75*i78 + 0.01627408*i75*i79 + 0.00784142*i75*i80 + 0.00564276*i75*i81 +
0.00324588*i75*i82 - 0.00767236*i75*i83 + 0.00699372*i75*i84 + 0.00737608*
i75*i85 + 0.00954642*i75*i86 + 0.00823136*i75*i87 + 0.0262748*i75*i88 +
0.00948902*i75*i89 + 0.01252876*i75*i90 + 0.01423104*i75*i91 + 0.00521492*
i75*i92 + 0.00397698*i75*i93 + 0.00422896*i75*i94 + 0.01025216*i75*i95 +
0.021456*i75*i96 + 0.01000128*i75*i97 + 0.00860654*i75*i98 + 0.0079023*i75
*i99 + 0.01223272*i75*i100 + 0.00508036*i76*i77 + 0.00440326*i76*i78 +
0.00722936*i76*i79 + 0.00592748*i76*i80 + 0.00543106*i76*i81 + 0.00352072*
i76*i82 + 0.00282876*i76*i83 + 0.00421804*i76*i84 + 0.00327576*i76*i85 +
0.00605002*i76*i86 + 0.00724932*i76*i87 + 0.01581762*i76*i88 + 0.00366428*
i76*i89 + 0.00812736*i76*i90 + 0.00388382*i76*i91 + 0.0047062*i76*i92 +
0.00287772*i76*i93 + 0.00297876*i76*i94 + 0.00459654*i76*i95 + 0.01070758*
i76*i96 + 0.0061617*i76*i97 + 0.00324936*i76*i98 + 0.00970994*i76*i99 +
0.00690694*i76*i100 + 0.00393188*i77*i78 + 0.00648912*i77*i79 + 0.00880144
*i77*i80 + 0.00990674*i77*i81 + 0.00277832*i77*i82 + 0.01369158*i77*i83 +
0.01108874*i77*i84 + 0.00804488*i77*i85 + 0.0100624*i77*i86 + 0.00868852*
i77*i87 + 0.0320896*i77*i88 + 0.00865688*i77*i89 + 0.00846622*i77*i90 +
0.01262084*i77*i91 + 0.01111726*i77*i92 + 0.00462154*i77*i93 + 0.00718072*
i77*i94 + 0.01147082*i77*i95 + 0.0176254*i77*i96 + 0.01224072*i77*i97 +
0.00939734*i77*i98 + 0.012534*i77*i99 + 0.01295098*i77*i100 + 0.00907912*
i78*i79 + 0.00720642*i78*i80 + 0.00426806*i78*i81 + 0.0028332*i78*i82 -
0.001354666*i78*i83 + 0.00318608*i78*i84 + 0.00627032*i78*i85 + 0.00574778
*i78*i86 + 0.00663794*i78*i87 + 0.00493084*i78*i88 + 0.00225816*i78*i89 +
0.01063042*i78*i90 + 0.0063342*i78*i91 + 0.00541402*i78*i92 + 0.00268782*
i78*i93 + 0.00290288*i78*i94 + 0.00588184*i78*i95 + 0.01436716*i78*i96 +
0.00728756*i78*i97 + 0.00442972*i78*i98 + 0.00924454*i78*i99 + 0.00979098*
i78*i100 + 0.0060581*i79*i80 + 0.00755126*i79*i81 + 0.00637932*i79*i82 -
0.00105651*i79*i83 + 0.01349704*i79*i84 + 0.01178354*i79*i85 + 0.0220208*
i79*i86 + 0.0245836*i79*i87 + 0.0524002*i79*i88 + 0.0230428*i79*i89 +
0.0314514*i79*i90 + 0.00636018*i79*i91 + 0.0061917*i79*i92 + 0.01207768*
i79*i93 + 0.00753416*i79*i94 + 0.01719794*i79*i95 + 0.0367202*i79*i96 +
0.01636496*i79*i97 + 0.01053626*i79*i98 + 0.0223148*i79*i99 + 0.0125583*
i79*i100 + 0.00731124*i80*i81 + 0.0043053*i80*i82 + 0.00250064*i80*i83 +
0.00942746*i80*i84 + 0.01109824*i80*i85 + 0.0094077*i80*i86 + 0.00584688*
i80*i87 + 0.01773876*i80*i88 + 0.00587054*i80*i89 + 0.0073899*i80*i90 +
0.01217556*i80*i91 + 0.0092825*i80*i92 + 0.001672258*i80*i93 + 0.00403362*
i80*i94 + 0.01001412*i80*i95 + 0.01641906*i80*i96 + 0.01159292*i80*i97 +
0.01062798*i80*i98 + 0.00967468*i80*i99 + 0.0140493*i80*i100 + 0.00288116*
i81*i82 + 0.022981*i81*i83 + 0.01105584*i81*i84 + 0.00722284*i81*i85 +
0.01178602*i81*i86 + 0.00945868*i81*i87 + 0.024973*i81*i88 + 0.00575624*
i81*i89 + 0.01415098*i81*i90 + 0.0066048*i81*i91 + 0.01072344*i81*i92 +
0.00322326*i81*i93 + 0.00351188*i81*i94 + 0.01127788*i81*i95 + 0.01956074*
i81*i96 + 0.01617428*i81*i97 + 0.0227228*i81*i98 + 0.01855842*i81*i99 +
0.01991896*i81*i100 - 0.00333172*i82*i83 + 0.00228114*i82*i84 + 0.00336158
*i82*i85 + 0.00354748*i82*i86 + 0.00514572*i82*i87 + 0.00636398*i82*i88 +
0.00276272*i82*i89 + 0.00394504*i82*i90 + 0.00242814*i82*i91 + 0.00151634*
i82*i92 + 0.00205258*i82*i93 + 0.00416174*i82*i94 + 0.0036601*i82*i95 +
0.00573294*i82*i96 + 0.0040347*i82*i97 + 0.001040396*i82*i98 + 0.00519918*
i82*i99 + 0.00479088*i82*i100 + 0.01497528*i83*i84 + 0.0032291*i83*i85 +
0.01011148*i83*i86 + 0.00471364*i83*i87 + 0.0246434*i83*i88 + 0.000996878*
i83*i89 - 0.00262512*i83*i90 - 0.000789784*i83*i91 + 0.01304756*i83*i92 +
0.000531142*i83*i93 - 0.000443948*i83*i94 + 0.00279848*i83*i95 - 0.0065326
*i83*i96 + 0.01221224*i83*i97 + 0.01799712*i83*i98 + 0.0158385*i83*i99 +
0.0071337*i83*i100 + 0.00892568*i84*i85 + 0.01364388*i84*i86 + 0.0072533*
i84*i87 + 0.0326884*i84*i88 + 0.00896504*i84*i89 + 0.00823562*i84*i90 +
0.0125821*i84*i91 + 0.00787816*i84*i92 + 0.00249586*i84*i93 + 0.00519262*
i84*i94 + 0.01044988*i84*i95 + 0.01107886*i84*i96 + 0.0139867*i84*i97 +
0.01596046*i84*i98 + 0.01218826*i84*i99 + 0.01543212*i84*i100 + 0.00990954
*i85*i86 + 0.00725662*i85*i87 + 0.0133432*i85*i88 + 0.00507396*i85*i89 +
0.00930526*i85*i90 + 0.01462284*i85*i91 + 0.01055408*i85*i92 + 0.00190258*
i85*i93 + 0.00468802*i85*i94 + 0.0107648*i85*i95 + 0.01646608*i85*i96 +
0.01215728*i85*i97 + 0.01028698*i85*i98 + 0.01183266*i85*i99 + 0.01660366*
i85*i100 + 0.0120373*i86*i87 + 0.0422718*i86*i88 + 0.00969238*i86*i89 +
0.01765146*i86*i90 + 0.01429788*i86*i91 + 0.0124585*i86*i92 + 0.0040945*
i86*i93 + 0.0046898*i86*i94 + 0.01232074*i86*i95 + 0.0222548*i86*i96 +
0.0145479*i86*i97 + 0.0128277*i86*i98 + 0.0192244*i86*i99 + 0.01947568*i86
*i100 + 0.032904*i87*i88 + 0.0084843*i87*i89 + 0.01591916*i87*i90 +
0.0059879*i87*i91 + 0.00789644*i87*i92 + 0.00607862*i87*i93 + 0.00667478*
i87*i94 + 0.0088746*i87*i95 + 0.01963916*i87*i96 + 0.01115822*i87*i97 +
0.0065973*i87*i98 + 0.01821046*i87*i99 + 0.01269924*i87*i100 + 0.04164*i88
*i89 + 0.01700894*i88*i90 + 0.0282218*i88*i91 + 0.0247666*i88*i92 +
0.00860626*i88*i93 + 0.0146832*i88*i94 + 0.0207292*i88*i95 + 0.0482992*i88
*i96 + 0.026772*i88*i97 + 0.0300758*i88*i98 + 0.0329128*i88*i99 +
0.01375988*i88*i100 + 0.00594302*i89*i90 + 0.00801468*i89*i91 + 0.00437824
*i89*i92 + 0.00302882*i89*i93 + 0.0041304*i89*i94 + 0.00803522*i89*i95 +
0.01620516*i89*i96 + 0.00836644*i89*i97 + 0.01022328*i89*i98 + 0.0069101*
i89*i99 + 0.00464412*i89*i100 + 0.01014268*i90*i91 + 0.00890216*i90*i92 +
0.00857494*i90*i93 + 0.00416286*i90*i94 + 0.01435266*i90*i95 + 0.038709*
i90*i96 + 0.01593092*i90*i97 + 0.0108455*i90*i98 + 0.0247362*i90*i99 +
0.0239224*i90*i100 + 0.01172504*i91*i92 - 3.25928e-5*i91*i93 + 0.00582154*
i91*i94 + 0.01455814*i91*i95 + 0.0217724*i91*i96 + 0.01520358*i91*i97 +
0.01361584*i91*i98 + 0.01107608*i91*i99 + 0.0218082*i91*i100 + 0.000834202
*i92*i93 + 0.00361846*i92*i94 + 0.00964536*i92*i95 + 0.01621624*i92*i96 +
0.01139352*i92*i97 + 0.01032652*i92*i98 + 0.01663626*i92*i99 + 0.01551254*
i92*i100 + 0.00302326*i93*i94 + 0.0039602*i93*i95 + 0.0070366*i93*i96 +
0.0035814*i93*i97 + 0.00156313*i93*i98 + 0.00599576*i93*i99 + 0.00427812*
i93*i100 + 0.00550244*i94*i95 + 0.00558508*i94*i96 + 0.0059384*i94*i97 +
0.00357124*i94*i98 + 0.0064057*i94*i99 + 0.00623724*i94*i100 + 0.0227304*
i95*i96 + 0.01445112*i95*i97 + 0.01257804*i95*i98 + 0.01368382*i95*i99 +
0.01773414*i95*i100 + 0.0257114*i96*i97 + 0.01933344*i96*i98 + 0.0317874*
i96*i99 + 0.0306278*i96*i100 + 0.01873902*i97*i98 + 0.01912542*i97*i99 +
0.0219022*i97*i100 + 0.01388668*i98*i99 + 0.0207524*i98*i100 + 0.0256994*
i99*i100 - objvar =L= 0;

e2..    0.00411438*i1 - 0.0186628*i2 - 0.0124176*i3 - 0.00587102*i4
- 0.0137519*i5 - 0.0174501*i6 - 0.0143449*i7 - 0.135908*i8 + 0.0183991*i9
- 0.00059102*i10 - 0.0458625*i11 + 0.00263166*i12 - 0.00331355*i13
- 0.0367972*i14 - 0.0139845*i15 - 0.0094868*i16 + 0.0248532*i17
- 0.0094023*i18 + 0.0023017*i19 - 0.0464684*i20 - 0.00593531*i21
- 0.00567252*i22 - 0.0053525*i23 - 0.0195131*i24 - 0.00539281*i25
+ 0.00014069*i26 - 0.0192418*i27 - 0.0094094*i28 - 0.00628791*i29
- 0.0640481*i30 + 0.00479685*i31 - 0.00773524*i32 - 0.0181879*i33
- 0.0252863*i34 - 0.0138439*i35 - 0.0175713*i36 - 0.0087821*i37
- 0.0159321*i38 - 0.0116042*i39 + 0.0157787*i40 - 0.0202007*i41
- 0.0126018*i42 - 0.00304129*i43 - 0.00993*i44 - 0.0128447*i45
- 0.00181865*i46 - 0.0158853*i47 - 0.00510726*i48 - 0.00213898*i49
- 0.030707*i50 + 0.00148868*i51 - 0.0125947*i52 - 0.00471196*i53
- 0.0148213*i54 - 0.00451418*i55 + 0.00107459*i56 - 0.00272748*i57
+ 0.00192127*i58 - 0.00643836*i59 + 0.00659625*i60 - 0.0160773*i61
- 0.0311089*i62 - 0.0220835*i63 - 0.0123205*i64 - 0.00688571*i65
- 0.0329356*i66 + 0.00327885*i67 - 0.009863*i68 - 0.0161333*i69
- 0.00415196*i70 - 0.0234616*i71 - 0.00105996*i72 + 0.00381383*i73
- 0.00073674*i74 - 0.0169568*i75 - 0.00559808*i76 - 0.0098104*i77
- 0.00457398*i78 - 0.0417583*i79 + 0.00283802*i80 - 0.0168204*i81
- 0.00228309*i82 - 0.0197823*i83 - 0.0100875*i84 - 0.0118258*i85
- 0.00342073*i86 - 0.00803049*i87 + 0.0213439*i88 - 0.0213604*i89
- 0.0139007*i90 - 0.0183623*i91 - 0.012037*i92 - 0.00197365*i93
- 0.0102456*i94 - 0.00369496*i95 - 0.00582019*i96 - 0.00227006*i97
- 0.0248562*i98 - 0.0205847*i99 - 0.0221142*i100 =G= 0;

e3..    52.59*i1 + 28.87*i2 + 29.19*i3 + 46.55*i4 + 24.26*i5 + 42.53*i6
+ 40.53*i7 + 79.56*i8 + 108.9*i9 + 79.06*i10 + 20.15*i11 + 35.64*i12
+ 39.55*i13 + 14.32*i14 + 26.41*i15 + 62.48*i16 + 254.3*i17 + 32.42*i18
+ 24.84*i19 + 10.1*i20 + 21.2*i21 + 40.25*i22 + 17.32*i23 + 60.92*i24
+ 54.73*i25 + 78.62*i26 + 49.24*i27 + 68.19*i28 + 50.3*i29 + 3.83*i30
+ 18.27*i31 + 59.67*i32 + 12.21*i33 + 38.09*i34 + 71.72*i35 + 23.6*i36
+ 70.71*i37 + 56.98*i38 + 34.47*i39 + 10.23*i40 + 59.19*i41 + 58.61*i42
+ 445.29*i43 + 131.69*i44 + 34.24*i45 + 43.11*i46 + 25.18*i47 + 28*i48
+ 19.43*i49 + 14.33*i50 + 28.41*i51 + 74.5*i52 + 36.54*i53 + 38.99*i54
+ 43.15*i55 + 199.55*i56 + 59.07*i57 + 123.55*i58 + 20.55*i59 + 66.72*i60
+ 37.95*i61 + 27.62*i62 + 23.21*i63 + 36.09*i64 + 23.09*i65 + 46.54*i66
+ 67.89*i67 + 34.83*i68 + 11.96*i69 + 45.77*i70 + 32.91*i71 + 77.37*i72
+ 21.46*i73 + 53.11*i74 + 14.29*i75 + 61.13*i76 + 32.79*i77 + 59.84*i78
+ 6.59*i79 + 14.06*i80 + 55.29*i81 + 33.33*i82 + 4.24*i83 + 23.21*i84
+ 47.85*i85 + 48.99*i86 + 57.46*i87 + 28.87*i88 + 24.6*i89 + 22.26*i90
+ 28.31*i91 + 26.67*i92 + 48.1*i93 + 28.01*i94 + 64.85*i95 + 25.54*i96
+ 31.47*i97 + 18.31*i98 + 35.06*i99 + 8.06*i100 =G= 10000;

e4..    52.59*i1 + 28.87*i2 + 29.19*i3 + 46.55*i4 + 24.26*i5 + 42.53*i6
+ 40.53*i7 + 79.56*i8 + 108.9*i9 + 79.06*i10 + 20.15*i11 + 35.64*i12
+ 39.55*i13 + 14.32*i14 + 26.41*i15 + 62.48*i16 + 254.3*i17 + 32.42*i18
+ 24.84*i19 + 10.1*i20 + 21.2*i21 + 40.25*i22 + 17.32*i23 + 60.92*i24
+ 54.73*i25 + 78.62*i26 + 49.24*i27 + 68.19*i28 + 50.3*i29 + 3.83*i30
+ 18.27*i31 + 59.67*i32 + 12.21*i33 + 38.09*i34 + 71.72*i35 + 23.6*i36
+ 70.71*i37 + 56.98*i38 + 34.47*i39 + 10.23*i40 + 59.19*i41 + 58.61*i42
+ 445.29*i43 + 131.69*i44 + 34.24*i45 + 43.11*i46 + 25.18*i47 + 28*i48
+ 19.43*i49 + 14.33*i50 + 28.41*i51 + 74.5*i52 + 36.54*i53 + 38.99*i54
+ 43.15*i55 + 199.55*i56 + 59.07*i57 + 123.55*i58 + 20.55*i59 + 66.72*i60
+ 37.95*i61 + 27.62*i62 + 23.21*i63 + 36.09*i64 + 23.09*i65 + 46.54*i66
+ 67.89*i67 + 34.83*i68 + 11.96*i69 + 45.77*i70 + 32.91*i71 + 77.37*i72
+ 21.46*i73 + 53.11*i74 + 14.29*i75 + 61.13*i76 + 32.79*i77 + 59.84*i78
+ 6.59*i79 + 14.06*i80 + 55.29*i81 + 33.33*i82 + 4.24*i83 + 23.21*i84
+ 47.85*i85 + 48.99*i86 + 57.46*i87 + 28.87*i88 + 24.6*i89 + 22.26*i90
+ 28.31*i91 + 26.67*i92 + 48.1*i93 + 28.01*i94 + 64.85*i95 + 25.54*i96
+ 31.47*i97 + 18.31*i98 + 35.06*i99 + 8.06*i100 =L= 11000;

* set non-default bounds

Model m / all /;

m.limrow=0; m.limcol=0;
m.tolproj=0.0;

\$if NOT '%gams.u1%' == '' \$include '%gams.u1%'

\$if not set MINLP \$set MINLP MINLP
Solve m using %MINLP% minimizing objvar;

```

Last updated: 2019-11-29 Git hash: 4a97e4ed