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Instance ex8_6_1
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | -44.99999952 (LINDO) |
| Referencesⓘ | Floudas, C A, Pardalos, Panos M, Adjiman, C S, Esposito, W R, Gumus, Zeynep H, Harding, S T, Klepeis, John L, Meyer, Clifford A, and Schweiger, C A, Handbook of Test Problems in Local and Global Optimization, Kluwer Academic Publishers, 1999. |
| Sourceⓘ | Test Problem ex8.6.1 of Chapter 8 of Floudas e.a. handbook |
| Added to libraryⓘ | 31 Jul 2001 |
| Problem typeⓘ | NLP |
| #Variablesⓘ | 75 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 75 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | polynomial |
| Objective curvatureⓘ | indefinite |
| #Nonzeros in Objectiveⓘ | 45 |
| #Nonlinear Nonzeros in Objectiveⓘ | 45 |
| #Constraintsⓘ | 45 |
| #Linear Constraintsⓘ | 0 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 45 |
| Operands in Gen. Nonlin. Functionsⓘ | div sqr |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 315 |
| #Nonlinear Nonzeros in Jacobianⓘ | 270 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 945 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 75 |
| #Blocks in Hessian of Lagrangianⓘ | 46 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 1 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 30 |
| Average blocksize in Hessian of Lagrangianⓘ | 1.630435 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e+00 |
| Maximal coefficientⓘ | 6.0000e+00 |
| Infeasibility of initial pointⓘ | 4.996e-16 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 46 46 0 0 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 76 76 0 0 0 0 0 0
* FX 6
*
* Nonzero counts
* Total const NL DLL
* 361 46 315 0
*
* Solve m using NLP minimizing objvar;
Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19
,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36
,x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52,x53
,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65,x66,x67,x68,x69,x70
,x71,x72,x73,x74,x75,objvar;
Equations e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19
,e20,e21,e22,e23,e24,e25,e26,e27,e28,e29,e30,e31,e32,e33,e34,e35,e36
,e37,e38,e39,e40,e41,e42,e43,e44,e45,e46;
e1.. -(POWER(x31,6) - 2*POWER(x31,3) + POWER(x32,6) - 2*POWER(x32,3) + POWER(
x33,6) - 2*POWER(x33,3) + POWER(x34,6) - 2*POWER(x34,3) + POWER(x35,6) - 2
*POWER(x35,3) + POWER(x36,6) - 2*POWER(x36,3) + POWER(x37,6) - 2*POWER(x37
,3) + POWER(x38,6) - 2*POWER(x38,3) + POWER(x39,6) - 2*POWER(x39,3) +
POWER(x40,6) - 2*POWER(x40,3) + POWER(x41,6) - 2*POWER(x41,3) + POWER(x42,
6) - 2*POWER(x42,3) + POWER(x43,6) - 2*POWER(x43,3) + POWER(x44,6) - 2*
POWER(x44,3) + POWER(x45,6) - 2*POWER(x45,3) + POWER(x46,6) - 2*POWER(x46,
3) + POWER(x47,6) - 2*POWER(x47,3) + POWER(x48,6) - 2*POWER(x48,3) +
POWER(x49,6) - 2*POWER(x49,3) + POWER(x50,6) - 2*POWER(x50,3) + POWER(x51,
6) - 2*POWER(x51,3) + POWER(x52,6) - 2*POWER(x52,3) + POWER(x53,6) - 2*
POWER(x53,3) + POWER(x54,6) - 2*POWER(x54,3) + POWER(x55,6) - 2*POWER(x55,
3) + POWER(x56,6) - 2*POWER(x56,3) + POWER(x57,6) - 2*POWER(x57,3) +
POWER(x58,6) - 2*POWER(x58,3) + POWER(x59,6) - 2*POWER(x59,3) + POWER(x60,
6) - 2*POWER(x60,3) + POWER(x61,6) - 2*POWER(x61,3) + POWER(x62,6) - 2*
POWER(x62,3) + POWER(x63,6) - 2*POWER(x63,3) + POWER(x64,6) - 2*POWER(x64,
3) + POWER(x65,6) - 2*POWER(x65,3) + POWER(x66,6) - 2*POWER(x66,3) +
POWER(x67,6) - 2*POWER(x67,3) + POWER(x68,6) - 2*POWER(x68,3) + POWER(x69,
6) - 2*POWER(x69,3) + POWER(x70,6) - 2*POWER(x70,3) + POWER(x71,6) - 2*
POWER(x71,3) + POWER(x72,6) - 2*POWER(x72,3) + POWER(x73,6) - 2*POWER(x73,
3) + POWER(x74,6) - 2*POWER(x74,3) + POWER(x75,6) - 2*POWER(x75,3))
+ objvar =E= 0;
e2.. -1/(sqr(x1 - x2) + sqr(x11 - x12) + sqr(x21 - x22)) + x31 =E= 0;
e3.. -1/(sqr(x1 - x3) + sqr(x11 - x13) + sqr(x21 - x23)) + x32 =E= 0;
e4.. -1/(sqr(x1 - x4) + sqr(x11 - x14) + sqr(x21 - x24)) + x33 =E= 0;
e5.. -1/(sqr(x1 - x5) + sqr(x11 - x15) + sqr(x21 - x25)) + x34 =E= 0;
e6.. -1/(sqr(x1 - x6) + sqr(x11 - x16) + sqr(x21 - x26)) + x35 =E= 0;
e7.. -1/(sqr(x1 - x7) + sqr(x11 - x17) + sqr(x21 - x27)) + x36 =E= 0;
e8.. -1/(sqr(x1 - x8) + sqr(x11 - x18) + sqr(x21 - x28)) + x37 =E= 0;
e9.. -1/(sqr(x1 - x9) + sqr(x11 - x19) + sqr(x21 - x29)) + x38 =E= 0;
e10.. -1/(sqr(x1 - x10) + sqr(x11 - x20) + sqr(x21 - x30)) + x39 =E= 0;
e11.. -1/(sqr(x2 - x3) + sqr(x12 - x13) + sqr(x22 - x23)) + x40 =E= 0;
e12.. -1/(sqr(x2 - x4) + sqr(x12 - x14) + sqr(x22 - x24)) + x41 =E= 0;
e13.. -1/(sqr(x2 - x5) + sqr(x12 - x15) + sqr(x22 - x25)) + x42 =E= 0;
e14.. -1/(sqr(x2 - x6) + sqr(x12 - x16) + sqr(x22 - x26)) + x43 =E= 0;
e15.. -1/(sqr(x2 - x7) + sqr(x12 - x17) + sqr(x22 - x27)) + x44 =E= 0;
e16.. -1/(sqr(x2 - x8) + sqr(x12 - x18) + sqr(x22 - x28)) + x45 =E= 0;
e17.. -1/(sqr(x2 - x9) + sqr(x12 - x19) + sqr(x22 - x29)) + x46 =E= 0;
e18.. -1/(sqr(x2 - x10) + sqr(x12 - x20) + sqr(x22 - x30)) + x47 =E= 0;
e19.. -1/(sqr(x3 - x4) + sqr(x13 - x14) + sqr(x23 - x24)) + x48 =E= 0;
e20.. -1/(sqr(x3 - x5) + sqr(x13 - x15) + sqr(x23 - x25)) + x49 =E= 0;
e21.. -1/(sqr(x3 - x6) + sqr(x13 - x16) + sqr(x23 - x26)) + x50 =E= 0;
e22.. -1/(sqr(x3 - x7) + sqr(x13 - x17) + sqr(x23 - x27)) + x51 =E= 0;
e23.. -1/(sqr(x3 - x8) + sqr(x13 - x18) + sqr(x23 - x28)) + x52 =E= 0;
e24.. -1/(sqr(x3 - x9) + sqr(x13 - x19) + sqr(x23 - x29)) + x53 =E= 0;
e25.. -1/(sqr(x3 - x10) + sqr(x13 - x20) + sqr(x23 - x30)) + x54 =E= 0;
e26.. -1/(sqr(x4 - x5) + sqr(x14 - x15) + sqr(x24 - x25)) + x55 =E= 0;
e27.. -1/(sqr(x4 - x6) + sqr(x14 - x16) + sqr(x24 - x26)) + x56 =E= 0;
e28.. -1/(sqr(x4 - x7) + sqr(x14 - x17) + sqr(x24 - x27)) + x57 =E= 0;
e29.. -1/(sqr(x4 - x8) + sqr(x14 - x18) + sqr(x24 - x28)) + x58 =E= 0;
e30.. -1/(sqr(x4 - x9) + sqr(x14 - x19) + sqr(x24 - x29)) + x59 =E= 0;
e31.. -1/(sqr(x4 - x10) + sqr(x14 - x20) + sqr(x24 - x30)) + x60 =E= 0;
e32.. -1/(sqr(x5 - x6) + sqr(x15 - x16) + sqr(x25 - x26)) + x61 =E= 0;
e33.. -1/(sqr(x5 - x7) + sqr(x15 - x17) + sqr(x25 - x27)) + x62 =E= 0;
e34.. -1/(sqr(x5 - x8) + sqr(x15 - x18) + sqr(x25 - x28)) + x63 =E= 0;
e35.. -1/(sqr(x5 - x9) + sqr(x15 - x19) + sqr(x25 - x29)) + x64 =E= 0;
e36.. -1/(sqr(x5 - x10) + sqr(x15 - x20) + sqr(x25 - x30)) + x65 =E= 0;
e37.. -1/(sqr(x6 - x7) + sqr(x16 - x17) + sqr(x26 - x27)) + x66 =E= 0;
e38.. -1/(sqr(x6 - x8) + sqr(x16 - x18) + sqr(x26 - x28)) + x67 =E= 0;
e39.. -1/(sqr(x6 - x9) + sqr(x16 - x19) + sqr(x26 - x29)) + x68 =E= 0;
e40.. -1/(sqr(x6 - x10) + sqr(x16 - x20) + sqr(x26 - x30)) + x69 =E= 0;
e41.. -1/(sqr(x7 - x8) + sqr(x17 - x18) + sqr(x27 - x28)) + x70 =E= 0;
e42.. -1/(sqr(x7 - x9) + sqr(x17 - x19) + sqr(x27 - x29)) + x71 =E= 0;
e43.. -1/(sqr(x7 - x10) + sqr(x17 - x20) + sqr(x27 - x30)) + x72 =E= 0;
e44.. -1/(sqr(x8 - x9) + sqr(x18 - x19) + sqr(x28 - x29)) + x73 =E= 0;
e45.. -1/(sqr(x8 - x10) + sqr(x18 - x20) + sqr(x28 - x30)) + x74 =E= 0;
e46.. -1/(sqr(x9 - x10) + sqr(x19 - x20) + sqr(x29 - x30)) + x75 =E= 0;
* set non-default bounds
x1.fx = 0;
x2.lo = -5; x2.up = 5;
x3.lo = -5; x3.up = 5;
x4.lo = -5; x4.up = 5;
x5.lo = -5; x5.up = 5;
x6.lo = -5; x6.up = 5;
x7.lo = -5; x7.up = 5;
x8.lo = -5; x8.up = 5;
x9.lo = -5; x9.up = 5;
x10.lo = -5; x10.up = 5;
x11.fx = 0;
x12.fx = 0;
x13.lo = -5; x13.up = 5;
x14.lo = -5; x14.up = 5;
x15.lo = -5; x15.up = 5;
x16.lo = -5; x16.up = 5;
x17.lo = -5; x17.up = 5;
x18.lo = -5; x18.up = 5;
x19.lo = -5; x19.up = 5;
x20.lo = -5; x20.up = 5;
x21.fx = 0;
x22.fx = 0;
x23.fx = 0;
x24.lo = -5; x24.up = 5;
x25.lo = -5; x25.up = 5;
x26.lo = -5; x26.up = 5;
x27.lo = -5; x27.up = 5;
x28.lo = -5; x28.up = 5;
x29.lo = -5; x29.up = 5;
x30.lo = -5; x30.up = 5;
* set non-default levels
x2.l = 3.43266708;
x3.l = 0.50375356;
x4.l = -1.98862096;
x5.l = -2.07787883;
x6.l = -2.75947133;
x7.l = -1.50169496;
x8.l = 3.56270347;
x9.l = -4.32886277;
x10.l = 0.00210668999999974;
x13.l = 4.91133039;
x14.l = 2.62250467;
x15.l = -3.69307517;
x16.l = 1.39718759;
x17.l = -3.40482136;
x18.l = -2.49919467;
x19.l = 1.68928609;
x20.l = -0.64643619;
x24.l = -3.49898212;
x25.l = 0.8911365;
x26.l = 3.30892812;
x27.l = -2.69184262;
x28.l = 1.6573446;
x29.l = 2.75857606;
x30.l = -1.96341523;
x31.l = 0.0848665660820583;
x32.l = 0.0410257523649882;
x33.l = 0.0433369072910337;
x34.l = 0.0533318858204364;
x35.l = 0.048742871418623;
x36.l = 0.0474070412149129;
x37.l = 0.0461135050589101;
x38.l = 0.0342436643329313;
x39.l = 0.234033993203568;
x40.l = 0.0305813197498946;
x41.l = 0.0206139788536328;
x42.l = 0.022321904556586;
x43.l = 0.019514587685195;
x44.l = 0.0231552480584656;
x45.l = 0.110991800051043;
x46.l = 0.0141433163490096;
x47.l = 0.06233782929589;
x48.l = 0.0422056151370249;
x49.l = 0.0122707298338899;
x50.l = 0.0294578214857431;
x51.l = 0.0124337559964587;
x52.l = 0.0149209531159923;
x53.l = 0.0241864337079319;
x54.l = 0.0285751692200051;
x55.l = 0.0169011255076456;
x56.l = 0.0206427090641815;
x57.l = 0.0268692752074436;
x58.l = 0.0119564718949588;
x59.l = 0.0219757698125455;
x60.l = 0.0587995371380756;
x61.l = 0.0310356025470503;
x62.l = 0.075455653192454;
x63.l = 0.0295607909263086;
x64.l = 0.0266495598227703;
x65.l = 0.0459626111078803;
x66.l = 0.0164878991409964;
x67.l = 0.0172772991007472;
x68.l = 0.350729712295995;
x69.l = 0.0252523239258106;
x70.l = 0.0220343327084997;
x71.l = 0.0157109506031469;
x72.l = 0.0961472396262811;
x73.l = 0.0123406666409974;
x74.l = 0.0342225900399961;
x75.l = 0.0215007077887895;
Model m / all /;
m.limrow=0; m.limcol=0;
m.tolproj=0.0;
$if NOT '%gams.u1%' == '' $include '%gams.u1%'
$if not set NLP $set NLP NLP
Solve m using %NLP% minimizing objvar;
Last updated: 2025-08-07 Git hash: e62cedfc