MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

Home // Instances // Documentation // Download // Statistics


Instance smallinvDAXr4b010-011

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.
Formats ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
0.39879750 p1 ( gdx sol )
(infeas: 0)
Other points (infeas > 1e-08)  
Dual Bounds
0.39879750 (ALPHAECP)
0.39879750 (ANTIGONE)
0.39879750 (BARON)
0.39879750 (BONMIN)
0.39879750 (COUENNE)
0.39879749 (CPLEX)
0.39879750 (GUROBI)
0.39879750 (LINDO)
0.39879750 (SCIP)
0.39879750 (SHOT)
Source POLIP instance portfolio/small-investor-MVO-DAX30-return_0.0040-budget_1000-1100
Application Portfolio Optimization
Added to library 26 Feb 2014
Problem type MIQCP
#Variables 31
#Binary Variables 0
#Integer Variables 30
#Nonlinear Variables 30
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 30
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 convex
#Nonzeros in Jacobian 121
#Nonlinear Nonzeros in Jacobian 30
#Nonzeros in (Upper-Left) Hessian of Lagrangian 900
#Nonzeros in Diagonal of Hessian of Lagrangian 30
#Blocks in Hessian of Lagrangian 1
Minimal blocksize in Hessian of Lagrangian 30
Maximal blocksize in Hessian of Lagrangian 30
Average blocksize in Hessian of Lagrangian 30.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 1.4252e-04
Maximal coefficient 1.0190e+02
Infeasibility of initial point 1000
Sparsity Jacobian Sparsity of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of 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
*         31        1        0       30        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        121       91       30        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,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;

Equations  e1,e2,e3,e4;


e1.. 0.00558391*sqr(i1) + 0.0103737*sqr(i2) + 0.0221075*sqr(i3) + 0.00399551*
     sqr(i4) + 0.00267064*sqr(i5) + 0.00516451*sqr(i6) + 0.00421051*sqr(i7) + 
     0.00368008*sqr(i8) + 0.00372788*sqr(i9) + 0.00668969*sqr(i10) + 0.00613034
     *sqr(i11) + 0.0129271*sqr(i12) + 0.00697595*sqr(i13) + 0.0104282*sqr(i14)
      + 0.00899168*sqr(i15) + 0.0206685*sqr(i16) + 0.0488863*sqr(i17) + 
     0.00894867*sqr(i18) + 0.0124118*sqr(i19) + 0.0122291*sqr(i20) + 0.0128973*
     sqr(i21) + 0.00668043*sqr(i22) + 0.0153425*sqr(i23) + 0.0128605*sqr(i24)
      + 0.00718697*sqr(i25) + 0.0102616*sqr(i26) + 0.0123235*sqr(i27) + 
     0.00569465*sqr(i28) + 0.00818114*sqr(i29) + 0.00469456*sqr(i30) + 
     0.00901964*i1*i2 + 0.00860972*i1*i3 + 0.00248004*i1*i4 + 0.001821292*i1*i5
      + 0.00561078*i1*i6 + 0.0051287*i1*i7 + 0.000691196*i1*i8 + 0.000805982*i1
     *i9 + 0.00531452*i1*i10 + 0.00556768*i1*i11 + 0.00745224*i1*i12 + 
     0.00478224*i1*i13 + 0.00610824*i1*i14 + 0.00577634*i1*i15 + 0.00613326*i1*
     i16 + 0.01432596*i1*i17 + 0.007501*i1*i18 + 0.00716212*i1*i19 + 0.00512922
     *i1*i20 + 0.0087283*i1*i21 + 0.00245846*i1*i22 + 0.0071572*i1*i23 + 
     0.00543966*i1*i24 + 0.00708258*i1*i25 + 0.00243422*i1*i26 + 0.00729094*i1*
     i27 + 0.00386642*i1*i28 + 0.0061908*i1*i29 + 0.00366754*i1*i30 + 
     0.01583972*i2*i3 + 0.00394608*i2*i4 + 0.001773554*i2*i5 + 0.00861376*i2*i6
      + 0.00604454*i2*i7 + 0.00312866*i2*i8 + 0.00184686*i2*i9 + 0.00924638*i2*
     i10 + 0.01131902*i2*i11 + 0.01253232*i2*i12 + 0.00675858*i2*i13 + 
     0.00804604*i2*i14 + 0.00869872*i2*i15 + 0.0094047*i2*i16 + 0.0251538*i2*
     i17 + 0.01321532*i2*i18 + 0.01127964*i2*i19 + 0.0096635*i2*i20 + 0.0160783
     *i2*i21 + 0.00271*i2*i22 + 0.01486022*i2*i23 + 0.01091018*i2*i24 + 
     0.01009426*i2*i25 + 0.00754144*i2*i26 + 0.01408844*i2*i27 + 0.00544162*i2*
     i28 + 0.01096178*i2*i29 + 0.00574964*i2*i30 + 0.00299428*i3*i4 + 
     0.001239314*i3*i5 + 0.01256412*i3*i6 + 0.00899714*i3*i7 + 0.00444448*i3*i8
      + 0.00616612*i3*i9 + 0.0146019*i3*i10 + 0.01249836*i3*i11 + 0.0264968*i3*
     i12 + 0.01266506*i3*i13 + 0.01358566*i3*i14 + 0.01419766*i3*i15 + 
     0.01033796*i3*i16 + 0.040104*i3*i17 + 0.01504214*i3*i18 + 0.0210518*i3*i19
      + 0.0169342*i3*i20 + 0.020394*i3*i21 + 0.006361*i3*i22 + 0.0173249*i3*i23
      + 0.01157254*i3*i24 + 0.01601196*i3*i25 + 0.01305808*i3*i26 + 0.018918*i3
     *i27 + 0.0100768*i3*i28 + 0.01415258*i3*i29 + 0.00890208*i3*i30 + 
     0.00365082*i4*i5 + 0.0031533*i4*i6 + 0.001664882*i4*i7 + 0.000487746*i4*i8
      + 0.00074873*i4*i9 + 0.00279536*i4*i10 + 0.000948078*i4*i11 + 0.00218644*
     i4*i12 + 0.001471884*i4*i13 + 0.001764448*i4*i14 + 0.001707856*i4*i15 + 
     0.00415534*i4*i16 + 0.00552118*i4*i17 + 0.00298928*i4*i18 + 0.000446818*i4
     *i19 + 0.0042709*i4*i20 + 0.00437068*i4*i21 + 0.001584414*i4*i22 + 
     0.0028495*i4*i23 + 0.00550266*i4*i24 + 0.0019381*i4*i25 - 0.000779792*i4*
     i26 + 0.00383714*i4*i27 + 0.00170793*i4*i28 + 0.00220852*i4*i29 + 
     0.001897386*i4*i30 + 0.00226608*i5*i6 + 0.001391572*i5*i7 + 0.001434726*i5
     *i8 + 0.000718962*i5*i9 + 0.00117417*i5*i10 + 0.001240914*i5*i11 + 
     0.000587866*i5*i12 + 0.0020154*i5*i13 + 0.00126883*i5*i14 + 0.000645164*i5
     *i15 + 0.0001425196*i5*i16 + 0.001199014*i5*i17 + 0.001896292*i5*i18 - 
     0.000289412*i5*i19 + 0.001457998*i5*i20 + 0.00199702*i5*i21 + 0.001266598*
     i5*i22 + 0.000764624*i5*i23 + 0.001961312*i5*i24 + 0.001748826*i5*i25 - 
     0.00122625*i5*i26 + 0.000753266*i5*i27 + 0.00063941*i5*i28 + 0.001644068*
     i5*i29 + 0.001587886*i5*i30 + 0.00454154*i6*i7 + 0.001157686*i6*i8 + 
     0.0032018*i6*i9 + 0.00727798*i6*i10 + 0.0064553*i6*i11 + 0.00791618*i6*i12
      + 0.00687526*i6*i13 + 0.00638032*i6*i14 + 0.00425538*i6*i15 + 0.00583332*
     i6*i16 + 0.01491304*i6*i17 + 0.00876772*i6*i18 + 0.00814434*i6*i19 + 
     0.00549208*i6*i20 + 0.0103848*i6*i21 + 0.001352278*i6*i22 + 0.0063097*i6*
     i23 + 0.0052012*i6*i24 + 0.00808494*i6*i25 + 0.00595234*i6*i26 + 
     0.00960786*i6*i27 + 0.0035648*i6*i28 + 0.00730486*i6*i29 + 0.0036145*i6*
     i30 + 0.0027426*i7*i8 + 0.00224138*i7*i9 + 0.00558948*i7*i10 + 0.00489378*
     i7*i11 + 0.0073565*i7*i12 + 0.0050794*i7*i13 + 0.00363244*i7*i14 + 
     0.00634576*i7*i15 + 0.001588982*i7*i16 + 0.00877926*i7*i17 + 0.00710862*i7
     *i18 + 0.00675396*i7*i19 + 0.00621206*i7*i20 + 0.00746652*i7*i21 + 
     0.001927036*i7*i22 + 0.00410122*i7*i23 + 0.00344774*i7*i24 + 0.00594546*i7
     *i25 + 0.00461784*i7*i26 + 0.00530234*i7*i27 + 0.00320122*i7*i28 + 
     0.00474356*i7*i29 + 0.00341222*i7*i30 + 0.00105347*i8*i9 + 0.001879822*i8*
     i10 + 0.00290244*i8*i11 + 0.00353818*i8*i12 + 0.0035513*i8*i13 + 
     0.00294406*i8*i14 + 0.00389942*i8*i15 + 0.00286866*i8*i16 + 0.000920126*i8
     *i17 + 0.00274282*i8*i18 + 0.0027675*i8*i19 + 0.00464592*i8*i20 + 
     0.001093444*i8*i21 + 0.000948594*i8*i22 + 0.00275316*i8*i23 + 0.001626794*
     i8*i24 + 0.00209498*i8*i25 + 0.0031962*i8*i26 + 0.001767658*i8*i27 + 
     0.00109948*i8*i28 + 0.00292004*i8*i29 + 0.00215496*i8*i30 + 0.00329222*i9*
     i10 + 0.00239978*i9*i11 + 0.00365066*i9*i12 + 0.00463422*i9*i13 + 
     0.00260888*i9*i14 + 0.00330432*i9*i15 + 0.000950274*i9*i16 + 0.00309664*i9
     *i17 + 0.00325462*i9*i18 + 0.00494078*i9*i19 + 0.00339202*i9*i20 + 
     0.00283784*i9*i21 + 0.001862472*i9*i22 + 0.001457294*i9*i23 + 0.000292408*
     i9*i24 + 0.00434258*i9*i25 + 0.0051917*i9*i26 + 0.00442724*i9*i27 + 
     0.00235362*i9*i28 + 0.0023207*i9*i29 + 0.00232972*i9*i30 + 0.00661128*i10*
     i11 + 0.0099349*i10*i12 + 0.00670728*i10*i13 + 0.00688756*i10*i14 + 
     0.00814804*i10*i15 + 0.00387536*i10*i16 + 0.01709622*i10*i17 + 0.00921546*
     i10*i18 + 0.01138012*i10*i19 + 0.0073598*i10*i20 + 0.012047*i10*i21 + 
     0.001953884*i10*i22 + 0.01110682*i10*i23 + 0.00744232*i10*i24 + 0.00846572
     *i10*i25 + 0.00811902*i10*i26 + 0.01093528*i10*i27 + 0.00642736*i10*i28 + 
     0.00817838*i10*i29 + 0.00467066*i10*i30 + 0.01089978*i11*i12 + 0.00580646*
     i11*i13 + 0.00479126*i11*i14 + 0.00655088*i11*i15 + 0.00784072*i11*i16 + 
     0.0171429*i11*i17 + 0.0099023*i11*i18 + 0.00881158*i11*i19 + 0.0065332*i11
     *i20 + 0.01111462*i11*i21 + 0.00238226*i11*i22 + 0.00942038*i11*i23 + 
     0.00509366*i11*i24 + 0.0079177*i11*i25 + 0.00653764*i11*i26 + 0.00963386*
     i11*i27 + 0.00518254*i11*i28 + 0.00839924*i11*i29 + 0.00396162*i11*i30 + 
     0.00812884*i12*i13 + 0.00932748*i12*i14 + 0.01172114*i12*i15 + 0.00937084*
     i12*i16 + 0.033621*i12*i17 + 0.0125625*i12*i18 + 0.01635358*i12*i19 + 
     0.01460644*i12*i20 + 0.01374474*i12*i21 + 0.00526496*i12*i22 + 0.01402198*
     i12*i23 + 0.00931776*i12*i24 + 0.01195866*i12*i25 + 0.00822682*i12*i26 + 
     0.01241788*i12*i27 + 0.00706034*i12*i28 + 0.01219462*i12*i29 + 0.00598988*
     i12*i30 + 0.0068538*i13*i14 + 0.00620178*i13*i15 + 0.00379406*i13*i16 + 
     0.00889862*i13*i17 + 0.00816594*i13*i18 + 0.01033824*i13*i19 + 0.00577162*
     i13*i20 + 0.00736548*i13*i21 + 0.00410776*i13*i22 + 0.00580558*i13*i23 + 
     0.00459074*i13*i24 + 0.0072167*i13*i25 + 0.00956086*i13*i26 + 0.00943468*
     i13*i27 + 0.00587164*i13*i28 + 0.00902842*i13*i29 + 0.00550608*i13*i30 + 
     0.00635356*i14*i15 + 0.00709628*i14*i16 + 0.01555038*i14*i17 + 0.00826722*
     i14*i18 + 0.00751614*i14*i19 + 0.00814342*i14*i20 + 0.00995652*i14*i21 + 
     0.00477798*i14*i22 + 0.0076843*i14*i23 + 0.00817698*i14*i24 + 0.00886056*
     i14*i25 + 0.00579636*i14*i26 + 0.01128084*i14*i27 + 0.00483444*i14*i28 + 
     0.0068342*i14*i29 + 0.0077372*i14*i30 + 0.00973548*i15*i16 + 0.01556958*
     i15*i17 + 0.00926266*i15*i18 + 0.01281188*i15*i19 + 0.00669072*i15*i20 + 
     0.00937684*i15*i21 + 0.00639856*i15*i22 + 0.00611934*i15*i23 + 0.00853942*
     i15*i24 + 0.00964296*i15*i25 + 0.00704584*i15*i26 + 0.0119279*i15*i27 + 
     0.00648174*i15*i28 + 0.01050128*i15*i29 + 0.00502696*i15*i30 + 0.01809222*
     i16*i17 + 0.00823288*i16*i18 + 0.01161214*i16*i19 + 0.00533676*i16*i20 + 
     0.01233794*i16*i21 + 0.00512778*i16*i22 + 0.00722276*i16*i23 + 0.01715638*
     i16*i24 + 0.00677738*i16*i25 + 0.0069565*i16*i26 + 0.01691522*i16*i27 + 
     0.00246824*i16*i28 + 0.00934088*i16*i29 + 0.00393866*i16*i30 + 0.01858542*
     i17*i18 + 0.0224912*i17*i19 + 0.01793624*i17*i20 + 0.0270204*i17*i21 + 
     0.01083832*i17*i22 + 0.0216678*i17*i23 + 0.0183347*i17*i24 + 0.01893*i17*
     i25 + 0.01089098*i17*i26 + 0.0209142*i17*i27 + 0.01273162*i17*i28 + 
     0.0200902*i17*i29 + 0.00774366*i17*i30 + 0.01171594*i18*i19 + 0.00861454*
     i18*i20 + 0.01414322*i18*i21 + 0.001961404*i18*i22 + 0.00910214*i18*i23 + 
     0.01003468*i18*i24 + 0.0094743*i18*i25 + 0.00825794*i18*i26 + 0.01336058*
     i18*i27 + 0.00607998*i18*i28 + 0.01070732*i18*i29 + 0.00492858*i18*i30 + 
     0.0082848*i19*i20 + 0.0126004*i19*i21 + 0.00407366*i19*i22 + 0.01381284*
     i19*i23 + 0.00838908*i19*i24 + 0.01198264*i19*i25 + 0.01583126*i19*i26 + 
     0.01664044*i19*i27 + 0.00924324*i19*i28 + 0.01214842*i19*i29 + 0.00592778*
     i19*i30 + 0.01071434*i20*i21 + 0.00296964*i20*i22 + 0.00736528*i20*i23 + 
     0.00606396*i20*i24 + 0.00628822*i20*i25 + 0.00817696*i20*i26 + 0.00776894*
     i20*i27 + 0.0026202*i20*i28 + 0.00717342*i20*i29 + 0.00579184*i20*i30 + 
     0.00469936*i21*i22 + 0.0138599*i21*i23 + 0.0125037*i21*i24 + 0.01211002*
     i21*i25 + 0.00836436*i21*i26 + 0.016494*i21*i27 + 0.00602872*i21*i28 + 
     0.01180462*i21*i29 + 0.00570478*i21*i30 + 0.0032176*i22*i23 + 0.00379112*
     i22*i24 + 0.00301976*i22*i25 + 0.00308424*i22*i26 + 0.00369962*i22*i27 + 
     0.00278784*i22*i28 + 0.00465846*i22*i29 + 0.00297212*i22*i30 + 0.01019176*
     i23*i24 + 0.00779098*i23*i25 + 0.00577776*i23*i26 + 0.01267514*i23*i27 + 
     0.00735432*i23*i28 + 0.00786386*i23*i29 + 0.00559972*i23*i30 + 0.00725022*
     i24*i25 + 0.00455648*i24*i26 + 0.0157223*i24*i27 + 0.00579512*i24*i28 + 
     0.00792398*i24*i29 + 0.0045755*i24*i30 + 0.00723442*i25*i26 + 0.01196012*
     i25*i27 + 0.0063273*i25*i28 + 0.0099815*i25*i29 + 0.0041794*i25*i30 + 
     0.01139894*i26*i27 + 0.0080092*i26*i28 + 0.0080044*i26*i29 + 0.00493602*
     i26*i30 + 0.00826208*i27*i28 + 0.01246152*i27*i29 + 0.0067556*i27*i30 + 
     0.00575648*i28*i29 + 0.0044929*i28*i30 + 0.00469952*i29*i30 - objvar =L= 0
     ;

e2..    0.00318236*i1 - 0.00015175*i2 - 0.00695114*i3 + 0.012626*i4
      + 0.0094202*i5 + 0.00596825*i6 + 0.00354677*i7 - 0.00134318*i8
      - 0.00670481*i9 - 0.00123195*i10 - 0.00051299*i11 - 0.00348068*i12
      + 0.00486372*i13 - 0.0102346*i14 - 0.00211219*i15 + 0.00457072*i16
      - 0.00828342*i17 - 0.00168175*i18 - 0.00531856*i19 - 0.00111388*i20
      + 0.0142599*i21 + 0.00545572*i22 + 0.0077442*i23 + 0.0195808*i24
      + 0.00260132*i25 - 0.00524596*i26 + 0.00306*i27 + 0.00329918*i28
      + 0.00265023*i29 + 0.0045383*i30 =G= 0;

e3..    39.19*i1 + 41.47*i2 + 5.71*i3 + 53.59*i4 + 43.65*i5 + 85.46*i6
      + 39.7*i7 + 44.91*i8 + 9.6*i9 + 11.26*i10 + 39.56*i11 + 46*i12
      + 45.25*i13 + 21.9*i14 + 11.85*i15 + 37.4*i16 + 4.75*i17 + 44.44*i18
      + 80.5*i19 + 49.46*i20 + 67.02*i21 + 59.25*i22 + 71.5*i23 + 48.8*i24
      + 73.22*i25 + 101.9*i26 + 20.06*i27 + 36.33*i28 + 41.31*i29 + 53.09*i30
      =G= 1000;

e4..    39.19*i1 + 41.47*i2 + 5.71*i3 + 53.59*i4 + 43.65*i5 + 85.46*i6
      + 39.7*i7 + 44.91*i8 + 9.6*i9 + 11.26*i10 + 39.56*i11 + 46*i12
      + 45.25*i13 + 21.9*i14 + 11.85*i15 + 37.4*i16 + 4.75*i17 + 44.44*i18
      + 80.5*i19 + 49.46*i20 + 67.02*i21 + 59.25*i22 + 71.5*i23 + 48.8*i24
      + 73.22*i25 + 101.9*i26 + 20.06*i27 + 36.33*i28 + 41.31*i29 + 53.09*i30
      =L= 1100;

* 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: 2022-05-24 Git hash: 1198c186
Imprint / Privacy Policy / License: CC-BY 4.0