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Instance maxmin

Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
-0.34108138 p1 ( gdx sol )
(infeas: 0)
-0.35036240 p2 ( gdx sol )
(infeas: 0)
-0.36609601 p3 ( gdx sol )
(infeas: 6e-17)
Other points (infeas > 1e-08)  
Dual Bounds
-1.09071382 (ANTIGONE)
-0.91659596 (BARON)
-1.04446594 (COUENNE)
-0.81568286 (LINDO)
-0.49349301 (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 of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of 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;


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