MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance ex8_3_9
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | -1.00000011 (ANTIGONE) -1.00000000 (BARON) -10.00000000 (COUENNE) -1.00000000 (GUROBI) -10.00000000 (LINDO) -10.00000000 (SCIP) |
| 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 ex8.3.9 of Chapter 8 of Floudas e.a. handbook |
| Added to libraryⓘ | 31 Jul 2001 |
| Problem typeⓘ | QCP |
| #Variablesⓘ | 78 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 73 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 1 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 45 |
| #Linear Constraintsⓘ | 18 |
| #Quadratic Constraintsⓘ | 27 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 325 |
| #Nonlinear Nonzeros in Jacobianⓘ | 214 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 184 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 0 |
| #Blocks in Hessian of Lagrangianⓘ | 16 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 2 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 9 |
| Average blocksize in Hessian of Lagrangianⓘ | 4.5625 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 4.5000e-01 |
| Maximal coefficientⓘ | 1.0000e+00 |
| Infeasibility of initial pointⓘ | 250 |
| 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
* 79 79 0 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 327 113 214 0
*
* Solve m using NLP minimizing objvar;
Variables objvar,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,x76,x77,x78,x79;
Positive Variables 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,x76,x77,x78,x79;
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.. - objvar - x69 =E= 0;
e2.. - x2 - x3 - x4 - x5 - x6 =E= -100;
e3.. - x2 + x7 - x37 - x42 - x47 - x52 - x57 =E= 0;
e4.. - x3 + x8 - x38 - x43 - x48 - x53 - x58 =E= 0;
e5.. - x4 + x9 - x39 - x44 - x49 - x54 - x59 =E= 0;
e6.. - x5 + x10 - x40 - x45 - x50 - x55 - x60 =E= 0;
e7.. - x6 + x11 - x41 - x46 - x51 - x56 - x61 =E= 0;
e8.. x12*x7 - (x27*x37 + x29*x42 + x31*x47 + x33*x52 + x35*x57) - 0.45*x2 =E= 0
;
e9.. x13*x7 - (x28*x37 + x30*x42 + x32*x47 + x34*x52 + x36*x57) - 0.55*x2 =E= 0
;
e10.. x14*x8 - (x27*x38 + x29*x43 + x31*x48 + x33*x53 + x35*x58) - 0.45*x3
=E= 0;
e11.. x15*x8 - (x28*x38 + x30*x43 + x32*x48 + x34*x53 + x36*x58) - 0.55*x3
=E= 0;
e12.. x16*x9 - (x27*x39 + x29*x44 + x31*x49 + x33*x54 + x35*x59) - 0.45*x4
=E= 0;
e13.. x17*x9 - (x28*x39 + x30*x44 + x32*x49 + x34*x54 + x36*x59) - 0.55*x4
=E= 0;
e14.. x18*x10 - (x27*x40 + x29*x45 + x31*x50 + x33*x55 + x35*x60) - 0.45*x5
=E= 0;
e15.. x19*x10 - (x28*x40 + x30*x45 + x32*x50 + x34*x55 + x36*x60) - 0.55*x5
=E= 0;
e16.. x20*x11 - (x27*x41 + x29*x46 + x31*x51 + x33*x56 + x35*x61) - 0.45*x6
=E= 0;
e17.. x21*x11 - (x28*x41 + x30*x46 + x32*x51 + x34*x56 + x36*x61) - 0.55*x6
=E= 0;
e18.. - x7 + x22 =E= 0;
e19.. - x8 + x23 =E= 0;
e20.. - x9 + x24 =E= 0;
e21.. - x10 + x25 =E= 0;
e22.. - x11 + x26 =E= 0;
e23.. x27*x22 - (x12*x7 - x70*x75) =E= 0;
e24.. x28*x22 - (x13*x7 + x70*x75) =E= 0;
e25.. x29*x23 - (x14*x8 - x71*x76) =E= 0;
e26.. x30*x23 - (x15*x8 + x71*x76) =E= 0;
e27.. x31*x24 - (x16*x9 - x72*x77) =E= 0;
e28.. x32*x24 - (x17*x9 + x72*x77) =E= 0;
e29.. x33*x25 - (x18*x10 - x73*x78) =E= 0;
e30.. x34*x25 - (x19*x10 + x73*x78) =E= 0;
e31.. x35*x26 - (x20*x11 - x74*x79) =E= 0;
e32.. x36*x26 - (x21*x11 + x74*x79) =E= 0;
e33.. -x27*x28 + x75 =E= 0;
e34.. -x29*x30 + x76 =E= 0;
e35.. -x31*x32 + x77 =E= 0;
e36.. -x33*x34 + x78 =E= 0;
e37.. -x35*x36 + x79 =E= 0;
e38.. x22 - x37 - x38 - x39 - x40 - x41 - x62 =E= 0;
e39.. x23 - x42 - x43 - x44 - x45 - x46 - x63 =E= 0;
e40.. x24 - x47 - x48 - x49 - x50 - x51 - x64 =E= 0;
e41.. x25 - x52 - x53 - x54 - x55 - x56 - x65 =E= 0;
e42.. x26 - x57 - x58 - x59 - x60 - x61 - x66 =E= 0;
e43.. - x62 - x63 - x64 - x65 - x66 + x67 =E= 0;
e44.. x67*x68 - (x62*x27 + x63*x29 + x64*x31 + x65*x33 + x66*x35) =E= 0;
e45.. x67*x69 - (x62*x28 + x63*x30 + x64*x32 + x65*x34 + x66*x36) =E= 0;
e46.. x70 + x71 + x72 + x73 + x74 =E= 100;
* set non-default bounds
x2.up = 1000;
x3.up = 1000;
x4.up = 1000;
x5.up = 1000;
x6.up = 1000;
x7.up = 1000;
x8.up = 1000;
x9.up = 1000;
x10.up = 1000;
x11.up = 1000;
x12.up = 10;
x13.up = 10;
x14.up = 10;
x15.up = 10;
x16.up = 10;
x17.up = 10;
x18.up = 10;
x19.up = 10;
x20.up = 10;
x21.up = 10;
x22.up = 1000;
x23.up = 1000;
x24.up = 1000;
x25.up = 1000;
x26.up = 1000;
x27.up = 10;
x28.up = 10;
x29.up = 10;
x30.up = 10;
x31.up = 10;
x32.up = 10;
x33.up = 10;
x34.up = 10;
x35.up = 10;
x36.up = 10;
x37.up = 1000;
x38.up = 1000;
x39.up = 1000;
x40.up = 1000;
x41.up = 1000;
x42.up = 1000;
x43.up = 1000;
x44.up = 1000;
x45.up = 1000;
x46.up = 1000;
x47.up = 1000;
x48.up = 1000;
x49.up = 1000;
x50.up = 1000;
x51.up = 1000;
x52.up = 1000;
x53.up = 1000;
x54.up = 1000;
x55.up = 1000;
x56.up = 1000;
x57.up = 1000;
x58.up = 1000;
x59.up = 1000;
x60.up = 1000;
x61.up = 1000;
x62.up = 1000;
x63.up = 1000;
x64.up = 1000;
x65.up = 1000;
x66.up = 1000;
x67.up = 1000;
x68.up = 10;
x69.up = 10;
x70.up = 10000;
x71.up = 10000;
x72.up = 10000;
x73.up = 10000;
x74.up = 10000;
x75.up = 10000;
x76.up = 10000;
x77.up = 10000;
x78.up = 10000;
x79.up = 10000;
* set non-default levels
x2.l = 50;
x3.l = 50;
x4.l = 50;
x5.l = 50;
x6.l = 50;
x7.l = 50;
x8.l = 50;
x9.l = 50;
x10.l = 50;
x11.l = 50;
x12.l = 0.2;
x13.l = 0.2;
x14.l = 0.2;
x15.l = 0.2;
x16.l = 0.2;
x17.l = 0.2;
x18.l = 0.2;
x19.l = 0.2;
x20.l = 0.2;
x21.l = 0.2;
x22.l = 100;
x23.l = 100;
x24.l = 100;
x25.l = 100;
x26.l = 100;
x27.l = 0.2;
x28.l = 0.2;
x29.l = 0.2;
x30.l = 0.2;
x31.l = 0.2;
x32.l = 0.2;
x33.l = 0.2;
x34.l = 0.2;
x35.l = 0.2;
x36.l = 0.2;
x37.l = 50;
x38.l = 50;
x39.l = 50;
x40.l = 50;
x41.l = 50;
x42.l = 50;
x43.l = 50;
x44.l = 50;
x45.l = 50;
x46.l = 50;
x47.l = 50;
x48.l = 50;
x49.l = 50;
x50.l = 50;
x51.l = 50;
x52.l = 50;
x53.l = 50;
x54.l = 50;
x55.l = 50;
x56.l = 50;
x57.l = 50;
x58.l = 50;
x59.l = 50;
x60.l = 50;
x61.l = 50;
x62.l = 50;
x63.l = 50;
x64.l = 50;
x65.l = 50;
x66.l = 50;
x67.l = 100;
x68.l = 0.2;
x69.l = 0.2;
x70.l = 1;
x71.l = 1;
x72.l = 1;
x73.l = 1;
x74.l = 1;
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