MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance st_rv8
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | -132.66162910 (ANTIGONE) -132.66162910 (BARON) -132.66162900 (COUENNE) -132.66162900 (CPLEX) -132.66162900 (GUROBI) -132.66162900 (LINDO) -132.66162960 (SCIP) |
| Referencesⓘ | Tawarmalani, M and Sahinidis, N V, Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications, Kluwer, 2002. Shectman, J P and Sahinidis, N V, A finite algorithm for global minimization of separable concave programs, Journal of Global Optimization, 12:1, 1998, 1-36. Shectman, J P, Finite Algorithms for Global Optimization of Concave Programs and General Quadratic Programs, PhD thesis, Department of Mechanical and Industrial Engineering, University of Illinois, Urbana Champagne, 1999. |
| Added to libraryⓘ | 03 Sep 2002 |
| Problem typeⓘ | QP |
| #Variablesⓘ | 40 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 40 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | quadratic |
| Objective curvatureⓘ | concave |
| #Nonzeros in Objectiveⓘ | 40 |
| #Nonlinear Nonzeros in Objectiveⓘ | 40 |
| #Constraintsⓘ | 20 |
| #Linear Constraintsⓘ | 20 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | linear |
| #Nonzeros in Jacobianⓘ | 320 |
| #Nonlinear Nonzeros in Jacobianⓘ | 0 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 40 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 40 |
| #Blocks in Hessian of Lagrangianⓘ | 40 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 1 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 1 |
| Average blocksize in Hessian of Lagrangianⓘ | 1.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 5.0000e-05 |
| Maximal coefficientⓘ | 9.0000e+00 |
| Infeasibility of initial pointⓘ | 0 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 21 1 0 20 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 41 41 0 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 361 321 40 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,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;
Equations e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19
,e20,e21;
e1.. 7*x1 + 4*x6 + 7*x7 + 6*x12 + 9*x13 + 2*x14 + x19 + 5*x20 + x25 + 5*x26
+ 3*x31 + 9*x32 + 5*x33 + x38 + x39 =L= 330;
e2.. 4*x1 + 7*x2 + 7*x7 + 8*x8 + 9*x13 + 3*x14 + 6*x15 + 2*x20 + 6*x21
+ 5*x26 + 3*x27 + 4*x32 + 6*x33 + 6*x34 + 6*x39 + 3*x40 =L= 425;
e3.. x2 + 6*x3 + 8*x8 + 7*x9 + 9*x14 + 8*x15 + 8*x16 + 6*x21 + 5*x22 + 4*x27
+ 2*x28 + 4*x33 + 7*x34 + 9*x35 + 2*x40 =L= 430;
e4.. x3 + 5*x4 + 9*x9 + 6*x10 + 4*x15 + 9*x16 + 6*x17 + 7*x22 + 9*x23
+ 8*x28 + 3*x29 + 7*x34 + 4*x35 + 3*x36 =L= 405;
e5.. 4*x4 + 7*x5 + 3*x10 + 6*x11 + 2*x16 + 8*x17 + 5*x18 + 2*x23 + 9*x24
+ 6*x29 + 4*x30 + 3*x35 + 6*x36 + 6*x37 =L= 355;
e6.. 5*x5 + 5*x6 + 7*x11 + 4*x12 + 4*x17 + 6*x18 + 2*x19 + 4*x24 + 2*x25
+ x30 + 4*x31 + 4*x36 + 3*x37 + 4*x38 =L= 275;
e7.. 2*x1 + 3*x6 + 3*x7 + 5*x12 + 9*x13 + 9*x18 + x19 + 4*x20 + 6*x25
+ 5*x26 + 3*x31 + 7*x32 + 3*x37 + 5*x38 + 4*x39 =L= 345;
e8.. 9*x1 + 7*x2 + 3*x7 + 6*x8 + 7*x13 + 2*x14 + x19 + x20 + 4*x21 + 5*x26
+ 2*x27 + 6*x32 + 5*x33 + 4*x38 + 4*x39 + 3*x40 =L= 345;
e9.. 6*x1 + 3*x2 + 4*x3 + 2*x8 + 7*x9 + 3*x14 + 7*x15 + 2*x20 + 3*x21
+ 2*x22 + 6*x27 + x28 + 6*x33 + 7*x34 + 9*x39 + 2*x40 =L= 350;
e10.. 2*x2 + 8*x3 + 9*x4 + x9 + x10 + 6*x15 + x16 + 6*x21 + 7*x22 + 6*x23
+ 3*x28 + 2*x29 + 7*x34 + 6*x35 + 5*x40 =L= 350;
e11.. 3*x3 + 6*x4 + 5*x5 + 6*x10 + 5*x11 + 8*x16 + 9*x17 + 6*x22 + 4*x23
+ x24 + 5*x29 + 2*x30 + 5*x35 + 4*x36 =L= 345;
e12.. 3*x4 + 3*x5 + 9*x6 + 3*x11 + 8*x12 + 9*x17 + 4*x18 + 4*x23 + 3*x24
+ 6*x25 + 6*x30 + x31 + 6*x36 + 2*x37 =L= 335;
e13.. 8*x5 + 2*x6 + 4*x7 + 8*x12 + 9*x13 + 3*x18 + 8*x19 + x24 + 8*x25
+ 8*x26 + 3*x31 + x32 + 5*x37 + 7*x38 =L= 375;
e14.. x1 + 9*x6 + x7 + 4*x8 + 9*x13 + 6*x14 + 6*x19 + 7*x20 + x25 + 5*x26
+ 7*x27 + x32 + 8*x33 + 9*x38 + 2*x39 =L= 380;
e15.. 3*x1 + 9*x2 + 4*x7 + 2*x8 + x9 + 3*x14 + 9*x15 + 7*x20 + 7*x21 + 8*x26
+ 7*x27 + 5*x28 + 4*x33 + x34 + 6*x39 + 9*x40 =L= 425;
e16.. 9*x2 + 6*x3 + 9*x8 + 5*x9 + 6*x10 + 6*x15 + 9*x16 + 5*x21 + 7*x22
+ 8*x27 + 7*x28 + x29 + x34 + 8*x35 + 4*x40 =L= 455;
e17.. 9*x3 + 9*x4 + 4*x9 + 2*x10 + 7*x11 + 4*x16 + 8*x17 + 3*x22 + 2*x23
+ 2*x28 + 7*x29 + 3*x30 + 4*x35 + 9*x36 =L= 365;
e18.. 5*x4 + 6*x5 + 8*x10 + 9*x11 + 6*x12 + 6*x17 + 4*x18 + 3*x23 + 3*x24
+ x29 + 9*x30 + 2*x31 + 4*x36 + 7*x37 =L= 365;
e19.. 5*x5 + 7*x6 + 2*x11 + 8*x12 + x13 + 9*x18 + 8*x19 + 6*x24 + x25
+ 4*x30 + 9*x31 + 7*x32 + 4*x37 + 6*x38 =L= 385;
e20.. 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 =L= 400;
e21.. -(-0.0004*sqr(x1) - 0.0384*x1 - 0.00285*sqr(x2) - 0.3876*x2 - 0.00155*
sqr(x3) - 0.1116*x3 - 0.0038*sqr(x4) - 0.4636*x4 - 0.0044*sqr(x5) - 0.044
*x5 - 0.0046*sqr(x6) - 0.3588*x6 - 0.00085*sqr(x7) - 0.0272*x7 - 0.00165*
sqr(x8) - 0.231*x8 - 0.0025*sqr(x9) - 0.27*x9 - 0.00385*sqr(x10) - 0.308*
x10 - 0.00355*sqr(x11) - 0.3692*x11 - 0.0015*sqr(x12) - 0.288*x12 -
0.0037*sqr(x13) - 0.407*x13 - 0.00125*sqr(x14) - 0.1175*x14 - 0.00095*
sqr(x15) - 0.1045*x15 - 0.0048*sqr(x16) - 0.1632*x16 - 0.0015*sqr(x17) -
0.135*x17 - 0.0037*sqr(x18) - 0.0666*x18 - 0.00125*sqr(x19) - 0.21*x19 -
0.00095*sqr(x20) - 0.1425*x20 - 0.0045*sqr(x21) - 0.882*x21 - 0.00245*
sqr(x22) - 0.3283*x22 - 0.0004*sqr(x23) - 0.0648*x23 - 0.0048*sqr(x24) -
0.0864*x24 - 0.00485*sqr(x25) - 0.4753*x25 - 0.00025*sqr(x26) - 0.046*x26
- 0.00435*sqr(x27) - 0.7917*x27 - 0.00365*sqr(x28) - 0.7008*x28 - 0.0002
*sqr(x29) - 0.0384*x29 - 0.00205*sqr(x30) - 0.0164*x30 - 0.00165*sqr(x31)
- 0.0891*x31 - 0.00175*sqr(x32) - 0.0945*x32 - 0.0048*sqr(x33) - 0.7296*
x33 - 5e-5*sqr(x34) - 0.0023*x34 - 0.00155*sqr(x35) - 0.1488*x35 -
0.00015*sqr(x36) - 0.0189*x36 - 0.00245*sqr(x37) - 0.0343*x37 - 0.00095*
sqr(x38) - 0.1045*x38 - 0.0038*sqr(x39) - 0.608*x39 - 0.0029*sqr(x40) -
0.0174*x40) + objvar =E= 0;
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