MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance maxmin
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | -1.09071382 (ANTIGONE) -0.71796852 (BARON) -1.04446594 (COUENNE) -1.04053536 (GUROBI) -0.81568286 (LINDO) -0.48806049 (SCIP) |
| Referencesⓘ | Stinstra, E, den Hertog, D, Stehouwer, P, and Vestjens, A, Constrained Maximin Designs for Computer Experiments, Technometrics, 45:4, 2003, 340-346. Pinter, J D, LGO - A Model Development System for Continuous Global Optimization, User's Guide, Pinter Consulting Services, Halifax, NS, Canada, Revised edition, 2003. |
| Sourceⓘ | GAMS Model Library model maxmin |
| Applicationⓘ | Geometry |
| Added to libraryⓘ | 31 Jul 2001 |
| Problem typeⓘ | NLP |
| #Variablesⓘ | 27 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 26 |
| #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ⓘ | 78 |
| #Linear Constraintsⓘ | 0 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 78 |
| Operands in Gen. Nonlin. Functionsⓘ | sqr sqrt |
| Constraints curvatureⓘ | nonconvex |
| #Nonzeros in Jacobianⓘ | 390 |
| #Nonlinear Nonzeros in Jacobianⓘ | 312 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 676 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 26 |
| #Blocks in Hessian of Lagrangianⓘ | 1 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 26 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 26 |
| Average blocksize in Hessian of Lagrangianⓘ | 26.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e+00 |
| Maximal coefficientⓘ | 1.0000e+00 |
| Infeasibility of initial pointⓘ | 0 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 78 0 0 78 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 27 27 0 0 0 0 0 0
* FX 2
*
* Nonzero counts
* Total const NL DLL
* 390 78 312 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,objvar;
Positive Variables x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18
,x19,x20,x21,x22,x23,x24,x25,x26;
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,e55,e56,e57,e58,e59,e60,e61,e62,e63,e64,e65,e66,e67,e68,e69,e70
,e71,e72,e73,e74,e75,e76,e77,e78;
e1.. -sqrt(sqr(x3 - x1) + sqr(x4 - x2)) - objvar =L= 0;
e2.. -sqrt(sqr(x5 - x1) + sqr(x6 - x2)) - objvar =L= 0;
e3.. -sqrt(sqr(x5 - x3) + sqr(x6 - x4)) - objvar =L= 0;
e4.. -sqrt(sqr(x7 - x1) + sqr(x8 - x2)) - objvar =L= 0;
e5.. -sqrt(sqr(x7 - x3) + sqr(x8 - x4)) - objvar =L= 0;
e6.. -sqrt(sqr(x7 - x5) + sqr(x8 - x6)) - objvar =L= 0;
e7.. -sqrt(sqr(x9 - x1) + sqr(x10 - x2)) - objvar =L= 0;
e8.. -sqrt(sqr(x9 - x3) + sqr(x10 - x4)) - objvar =L= 0;
e9.. -sqrt(sqr(x9 - x5) + sqr(x10 - x6)) - objvar =L= 0;
e10.. -sqrt(sqr(x9 - x7) + sqr(x10 - x8)) - objvar =L= 0;
e11.. -sqrt(sqr(x11 - x1) + sqr(x12 - x2)) - objvar =L= 0;
e12.. -sqrt(sqr(x11 - x3) + sqr(x12 - x4)) - objvar =L= 0;
e13.. -sqrt(sqr(x11 - x5) + sqr(x12 - x6)) - objvar =L= 0;
e14.. -sqrt(sqr(x11 - x7) + sqr(x12 - x8)) - objvar =L= 0;
e15.. -sqrt(sqr(x11 - x9) + sqr(x12 - x10)) - objvar =L= 0;
e16.. -sqrt(sqr(x13 - x1) + sqr(x14 - x2)) - objvar =L= 0;
e17.. -sqrt(sqr(x13 - x3) + sqr(x14 - x4)) - objvar =L= 0;
e18.. -sqrt(sqr(x13 - x5) + sqr(x14 - x6)) - objvar =L= 0;
e19.. -sqrt(sqr(x13 - x7) + sqr(x14 - x8)) - objvar =L= 0;
e20.. -sqrt(sqr(x13 - x9) + sqr(x14 - x10)) - objvar =L= 0;
e21.. -sqrt(sqr(x13 - x11) + sqr(x14 - x12)) - objvar =L= 0;
e22.. -sqrt(sqr(x15 - x1) + sqr(x16 - x2)) - objvar =L= 0;
e23.. -sqrt(sqr(x15 - x3) + sqr(x16 - x4)) - objvar =L= 0;
e24.. -sqrt(sqr(x15 - x5) + sqr(x16 - x6)) - objvar =L= 0;
e25.. -sqrt(sqr(x15 - x7) + sqr(x16 - x8)) - objvar =L= 0;
e26.. -sqrt(sqr(x15 - x9) + sqr(x16 - x10)) - objvar =L= 0;
e27.. -sqrt(sqr(x15 - x11) + sqr(x16 - x12)) - objvar =L= 0;
e28.. -sqrt(sqr(x15 - x13) + sqr(x16 - x14)) - objvar =L= 0;
e29.. -sqrt(sqr(x17 - x1) + sqr(x18 - x2)) - objvar =L= 0;
e30.. -sqrt(sqr(x17 - x3) + sqr(x18 - x4)) - objvar =L= 0;
e31.. -sqrt(sqr(x17 - x5) + sqr(x18 - x6)) - objvar =L= 0;
e32.. -sqrt(sqr(x17 - x7) + sqr(x18 - x8)) - objvar =L= 0;
e33.. -sqrt(sqr(x17 - x9) + sqr(x18 - x10)) - objvar =L= 0;
e34.. -sqrt(sqr(x17 - x11) + sqr(x18 - x12)) - objvar =L= 0;
e35.. -sqrt(sqr(x17 - x13) + sqr(x18 - x14)) - objvar =L= 0;
e36.. -sqrt(sqr(x17 - x15) + sqr(x18 - x16)) - objvar =L= 0;
e37.. -sqrt(sqr(x19 - x1) + sqr(x20 - x2)) - objvar =L= 0;
e38.. -sqrt(sqr(x19 - x3) + sqr(x20 - x4)) - objvar =L= 0;
e39.. -sqrt(sqr(x19 - x5) + sqr(x20 - x6)) - objvar =L= 0;
e40.. -sqrt(sqr(x19 - x7) + sqr(x20 - x8)) - objvar =L= 0;
e41.. -sqrt(sqr(x19 - x9) + sqr(x20 - x10)) - objvar =L= 0;
e42.. -sqrt(sqr(x19 - x11) + sqr(x20 - x12)) - objvar =L= 0;
e43.. -sqrt(sqr(x19 - x13) + sqr(x20 - x14)) - objvar =L= 0;
e44.. -sqrt(sqr(x19 - x15) + sqr(x20 - x16)) - objvar =L= 0;
e45.. -sqrt(sqr(x19 - x17) + sqr(x20 - x18)) - objvar =L= 0;
e46.. -sqrt(sqr(x21 - x1) + sqr(x22 - x2)) - objvar =L= 0;
e47.. -sqrt(sqr(x21 - x3) + sqr(x22 - x4)) - objvar =L= 0;
e48.. -sqrt(sqr(x21 - x5) + sqr(x22 - x6)) - objvar =L= 0;
e49.. -sqrt(sqr(x21 - x7) + sqr(x22 - x8)) - objvar =L= 0;
e50.. -sqrt(sqr(x21 - x9) + sqr(x22 - x10)) - objvar =L= 0;
e51.. -sqrt(sqr(x21 - x11) + sqr(x22 - x12)) - objvar =L= 0;
e52.. -sqrt(sqr(x21 - x13) + sqr(x22 - x14)) - objvar =L= 0;
e53.. -sqrt(sqr(x21 - x15) + sqr(x22 - x16)) - objvar =L= 0;
e54.. -sqrt(sqr(x21 - x17) + sqr(x22 - x18)) - objvar =L= 0;
e55.. -sqrt(sqr(x21 - x19) + sqr(x22 - x20)) - objvar =L= 0;
e56.. -sqrt(sqr(x23 - x1) + sqr(x24 - x2)) - objvar =L= 0;
e57.. -sqrt(sqr(x23 - x3) + sqr(x24 - x4)) - objvar =L= 0;
e58.. -sqrt(sqr(x23 - x5) + sqr(x24 - x6)) - objvar =L= 0;
e59.. -sqrt(sqr(x23 - x7) + sqr(x24 - x8)) - objvar =L= 0;
e60.. -sqrt(sqr(x23 - x9) + sqr(x24 - x10)) - objvar =L= 0;
e61.. -sqrt(sqr(x23 - x11) + sqr(x24 - x12)) - objvar =L= 0;
e62.. -sqrt(sqr(x23 - x13) + sqr(x24 - x14)) - objvar =L= 0;
e63.. -sqrt(sqr(x23 - x15) + sqr(x24 - x16)) - objvar =L= 0;
e64.. -sqrt(sqr(x23 - x17) + sqr(x24 - x18)) - objvar =L= 0;
e65.. -sqrt(sqr(x23 - x19) + sqr(x24 - x20)) - objvar =L= 0;
e66.. -sqrt(sqr(x23 - x21) + sqr(x24 - x22)) - objvar =L= 0;
e67.. -sqrt(sqr(x25 - x1) + sqr(x26 - x2)) - objvar =L= 0;
e68.. -sqrt(sqr(x25 - x3) + sqr(x26 - x4)) - objvar =L= 0;
e69.. -sqrt(sqr(x25 - x5) + sqr(x26 - x6)) - objvar =L= 0;
e70.. -sqrt(sqr(x25 - x7) + sqr(x26 - x8)) - objvar =L= 0;
e71.. -sqrt(sqr(x25 - x9) + sqr(x26 - x10)) - objvar =L= 0;
e72.. -sqrt(sqr(x25 - x11) + sqr(x26 - x12)) - objvar =L= 0;
e73.. -sqrt(sqr(x25 - x13) + sqr(x26 - x14)) - objvar =L= 0;
e74.. -sqrt(sqr(x25 - x15) + sqr(x26 - x16)) - objvar =L= 0;
e75.. -sqrt(sqr(x25 - x17) + sqr(x26 - x18)) - objvar =L= 0;
e76.. -sqrt(sqr(x25 - x19) + sqr(x26 - x20)) - objvar =L= 0;
e77.. -sqrt(sqr(x25 - x21) + sqr(x26 - x22)) - objvar =L= 0;
e78.. -sqrt(sqr(x25 - x23) + sqr(x26 - x24)) - objvar =L= 0;
* set non-default bounds
x1.fx = 0;
x2.fx = 0;
x3.up = 1;
x4.up = 1;
x5.up = 1;
x6.up = 1;
x7.up = 1;
x8.up = 1;
x9.up = 1;
x10.up = 1;
x11.up = 1;
x12.up = 1;
x13.up = 1;
x14.up = 1;
x15.up = 1;
x16.up = 1;
x17.up = 1;
x18.up = 1;
x19.up = 1;
x20.up = 1;
x21.up = 1;
x22.up = 1;
x23.up = 1;
x24.up = 1;
x25.up = 1;
x26.up = 1;
* set non-default levels
x3.l = 0.550375356;
x4.l = 0.301137904;
x5.l = 0.292212117;
x6.l = 0.224052867;
x7.l = 0.349830504;
x8.l = 0.856270347;
x9.l = 0.067113723;
x10.l = 0.500210669;
x11.l = 0.998117627;
x12.l = 0.578733378;
x13.l = 0.991133039;
x14.l = 0.762250467;
x15.l = 0.130692483;
x16.l = 0.639718759;
x17.l = 0.159517864;
x18.l = 0.250080533;
x19.l = 0.668928609;
x20.l = 0.435356381;
x21.l = 0.359700266;
x22.l = 0.351441368;
x23.l = 0.13149159;
x24.l = 0.150101788;
x25.l = 0.58911365;
x26.l = 0.830892812;
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