MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance ex5_3_3
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 2.39959800 (ANTIGONE) 2.47297011 (BARON) 2.27735184 (COUENNE) 3.23401821 (GUROBI) 2.11075015 (LINDO) 3.04869563 (SCIP) 1.63131800 (SHOT) |
| 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. Aggarwal, Avanish and Floudas, C A, Synthesis of General Distillation Sequences - Nonsharp Separations, Computers and Chemical Engineering, 14:6, 1990, 631-653. |
| Sourceⓘ | Test Problem ex5.3.3 of Chapter 5 of Floudas e.a. handbook |
| Added to libraryⓘ | 31 Jul 2001 |
| Problem typeⓘ | QCQP |
| #Variablesⓘ | 62 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 51 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | quadratic |
| Objective curvatureⓘ | indefinite |
| #Nonzeros in Objectiveⓘ | 12 |
| #Nonlinear Nonzeros in Objectiveⓘ | 12 |
| #Constraintsⓘ | 53 |
| #Linear Constraintsⓘ | 19 |
| #Quadratic Constraintsⓘ | 34 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 275 |
| #Nonlinear Nonzeros in Jacobianⓘ | 188 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 140 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 0 |
| #Blocks in Hessian of Lagrangianⓘ | 9 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 4 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 8 |
| Average blocksize in Hessian of Lagrangianⓘ | 5.666667 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 9.4070e-05 |
| Maximal coefficientⓘ | 1.0000e+00 |
| Infeasibility of initial pointⓘ | 600 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 54 54 0 0 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 63 63 0 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 288 88 200 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,objvar;
Positive 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;
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,e47,e48,e49,e50,e51,e52,e53
,e54;
e1.. x1 + x2 + x3 + x4 + x5 =E= 600;
e2.. - x1 + x6 - x17 - x26 =E= 0;
e3.. - x2 - x11 + x15 - x27 =E= 0;
e4.. - x3 - x12 - x21 + x24 =E= 0;
e5.. x7 - x8 - x9 =E= 0;
e6.. x10 - x11 - x12 - x13 - x14 =E= 0;
e7.. x16 - x17 - x18 - x19 =E= 0;
e8.. x20 - x21 - x22 - x23 =E= 0;
e9.. x25 - x26 - x27 - x28 - x29 =E= 0;
e10.. x30 - x31 - x32 =E= 0;
e11.. x7*x37 - 0.85*x6*x33 =E= 0;
e12.. x16*x48 - 0.85*x15*x44 =E= 0;
e13.. x25*x59 - x24*x55 =E= 0;
e14.. x10*x40 - x6*x34 =E= 0;
e15.. x20*x51 - 0.85*x15*x45 =E= 0;
e16.. x30*x62 - 0.85*x24*x56 =E= 0;
e17.. x6*x33 - x7*x37 - x10*x39 =E= 0;
e18.. x6*x34 - x7*x38 - x10*x40 =E= 0;
e19.. x6*x35 - x10*x41 =E= 0;
e20.. x6*x36 - x10*x42 =E= 0;
e21.. x15*x43 - x16*x47 =E= 0;
e22.. x15*x44 - x16*x48 - x20*x50 =E= 0;
e23.. x15*x45 - x16*x49 - x20*x51 =E= 0;
e24.. x15*x46 - x20*x52 =E= 0;
e25.. x24*x53 - x25*x57 =E= 0;
e26.. x24*x54 - x25*x58 =E= 0;
e27.. x24*x55 - x25*x59 - x30*x61 =E= 0;
e28.. x24*x56 - x25*x60 - x30*x62 =E= 0;
e29.. x17*x47 + x26*x57 - x6*x33 + 0.25*x1 =E= 0;
e30.. x17*x48 + x26*x58 - x6*x34 + 0.333*x1 =E= 0;
e31.. x17*x49 + x26*x59 - x6*x35 + 0.167*x1 =E= 0;
e32.. x26*x60 - x6*x36 + 0.25*x1 =E= 0;
e33.. x11*x39 + x27*x57 - x15*x43 + 0.25*x2 =E= 0;
e34.. x11*x40 + x27*x58 - x15*x44 + 0.333*x2 =E= 0;
e35.. x11*x41 + x27*x59 - x15*x45 + 0.167*x2 =E= 0;
e36.. x11*x42 + x27*x60 - x15*x46 + 0.25*x2 =E= 0;
e37.. x12*x39 - x24*x53 + 0.25*x3 =E= 0;
e38.. x12*x40 + x21*x50 - x24*x54 + 0.333*x3 =E= 0;
e39.. x12*x41 + x21*x51 - x24*x55 + 0.167*x3 =E= 0;
e40.. x12*x42 + x21*x52 - x24*x56 + 0.25*x3 =E= 0;
e41.. x8*x37 + x13*x39 + x18*x47 + x28*x57 + 0.25*x4 =E= 50;
e42.. x8*x38 + x13*x40 + x18*x48 + x22*x50 + x28*x58 + 0.222*x4 =E= 100;
e43.. x13*x41 + x18*x49 + x22*x51 + x28*x59 + x31*x61 + 0.167*x4 =E= 40;
e44.. x13*x42 + x22*x52 + x28*x60 + x31*x62 + 0.25*x4 =E= 100;
e45.. x33 + x34 + x35 + x36 =E= 1;
e46.. x37 + x38 =E= 1;
e47.. x39 + x40 + x41 + x42 =E= 1;
e48.. x43 + x44 + x45 + x46 =E= 1;
e49.. x47 + x48 + x49 =E= 1;
e50.. x50 + x51 + x52 =E= 1;
e51.. x53 + x54 + x55 + x56 =E= 1;
e52.. x57 + x58 + x59 + x60 =E= 1;
e53.. x61 + x62 =E= 1;
e54.. -((0.00132223 + 0.0016446*x33 + 0.0018611*x34 + 0.001262*x35)*x6 + (-
9.40700000000017e-5 + 0.0015625*x43 + 0.0091604*x44 + 0.0076758*x45)*x15
+ (0.00457315 - 0.001748*x53 - 0.0002583*x54 - 0.0004691*x55)*x24)
+ objvar =E= 1.68776;
* set non-default bounds
x1.up = 600;
x2.up = 600;
x3.up = 600;
x4.up = 600;
x5.up = 600;
x6.up = 600;
x7.up = 600;
x8.up = 600;
x9.up = 600;
x10.up = 600;
x11.up = 600;
x12.up = 600;
x13.up = 600;
x14.up = 600;
x15.up = 600;
x16.up = 600;
x17.up = 600;
x18.up = 600;
x19.up = 600;
x20.up = 600;
x21.up = 600;
x22.up = 600;
x23.up = 600;
x24.up = 600;
x25.up = 600;
x26.up = 600;
x27.up = 600;
x28.up = 600;
x29.up = 600;
x30.up = 600;
x31.up = 600;
x32.up = 600;
x33.up = 1;
x34.up = 1;
x35.up = 1;
x36.up = 1;
x37.up = 1;
x38.up = 1;
x39.up = 1;
x40.up = 1;
x41.up = 1;
x42.up = 1;
x43.up = 1;
x44.up = 1;
x45.up = 1;
x46.up = 1;
x47.up = 1;
x48.up = 1;
x49.up = 1;
x50.up = 1;
x51.up = 1;
x52.up = 1;
x53.up = 1;
x54.up = 1;
x55.up = 1;
x56.up = 1;
x57.up = 1;
x58.up = 1;
x59.up = 1;
x60.up = 1;
x61.up = 1;
x62.up = 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: 2024-12-17 Git hash: 8eaceb91