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Instance: ex8_6_2

Formats ams gms mod nl osil
Primal Bounds
-26.77844871 p1 ( gdx sol )
(infeas: 0)
-31.88862963 p2 ( gdx sol )
(infeas: 0)
Dual Bounds
-45.00000000 (ANTIGONE)
-45.00000000 (BARON)
-45.00000003 (COUENNE)
-45.00000000 (LINDO)
-45.00000000 (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 ex8.6.2 of Chapter 8 of Floudas e.a. handbook
Added to library 31 Jul 2001
Problem type NLP
#Variables 30
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 30
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type nonlinear
Objective curvature nonconvex
#Nonzeros in Objective 30
#Nonlinear Nonzeros in Objective 30
#Constraints 0
#Linear Constraints 0
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions sqr vcpower exp
Constraints curvature linear
#Nonzeros in Jacobian 0
#Nonlinear Nonzeros in Jacobian 0
#Nonzeros in (Upper-Left) Hessian of Lagrangian 900
#Nonzeros in Diagonal of Hessian of Lagrangian 30
#Blocks in Hessian of Lagrangian 1
Minimal blocksize in Hessian of Lagrangian 30
Maximal blocksize in Hessian of Lagrangian 30
Average blocksize in Hessian of Lagrangian 30.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
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
*          1        1        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         31       31        0        0        0        0        0        0
*  FX      6
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         31        1       30        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,objvar;

Equations  e1;


e1.. -(sqr(1 - exp(3 - 3*(sqr(x1 - x2) + sqr(x11 - x12) + sqr(x21 - x22))**0.5)
     ) + sqr(1 - exp(3 - 3*(sqr(x1 - x3) + sqr(x11 - x13) + sqr(x21 - x23))**
     0.5)) + sqr(1 - exp(3 - 3*(sqr(x1 - x4) + sqr(x11 - x14) + sqr(x21 - x24))
     **0.5)) + sqr(1 - exp(3 - 3*(sqr(x1 - x5) + sqr(x11 - x15) + sqr(x21 - x25
     ))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x1 - x6) + sqr(x11 - x16) + sqr(x21 - 
     x26))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x1 - x7) + sqr(x11 - x17) + sqr(x21
      - x27))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x1 - x8) + sqr(x11 - x18) + sqr(
     x21 - x28))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x1 - x9) + sqr(x11 - x19) + 
     sqr(x21 - x29))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x1 - x10) + sqr(x11 - x20)
      + sqr(x21 - x30))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x2 - x3) + sqr(x12 - 
     x13) + sqr(x22 - x23))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x2 - x4) + sqr(x12
      - x14) + sqr(x22 - x24))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x2 - x5) + sqr(
     x12 - x15) + sqr(x22 - x25))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x2 - x6) + 
     sqr(x12 - x16) + sqr(x22 - x26))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x2 - x7)
      + sqr(x12 - x17) + sqr(x22 - x27))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x2 - 
     x8) + sqr(x12 - x18) + sqr(x22 - x28))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x2
      - x9) + sqr(x12 - x19) + sqr(x22 - x29))**0.5)) + sqr(1 - exp(3 - 3*(sqr(
     x2 - x10) + sqr(x12 - x20) + sqr(x22 - x30))**0.5)) + sqr(1 - exp(3 - 3*(
     sqr(x3 - x4) + sqr(x13 - x14) + sqr(x23 - x24))**0.5)) + sqr(1 - exp(3 - 3
     *(sqr(x3 - x5) + sqr(x13 - x15) + sqr(x23 - x25))**0.5)) + sqr(1 - exp(3
      - 3*(sqr(x3 - x6) + sqr(x13 - x16) + sqr(x23 - x26))**0.5)) + sqr(1 - 
     exp(3 - 3*(sqr(x3 - x7) + sqr(x13 - x17) + sqr(x23 - x27))**0.5)) + sqr(1
      - exp(3 - 3*(sqr(x3 - x8) + sqr(x13 - x18) + sqr(x23 - x28))**0.5)) + 
     sqr(1 - exp(3 - 3*(sqr(x3 - x9) + sqr(x13 - x19) + sqr(x23 - x29))**0.5))
      + sqr(1 - exp(3 - 3*(sqr(x3 - x10) + sqr(x13 - x20) + sqr(x23 - x30))**
     0.5)) + sqr(1 - exp(3 - 3*(sqr(x4 - x5) + sqr(x14 - x15) + sqr(x24 - x25))
     **0.5)) + sqr(1 - exp(3 - 3*(sqr(x4 - x6) + sqr(x14 - x16) + sqr(x24 - x26
     ))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x4 - x7) + sqr(x14 - x17) + sqr(x24 - 
     x27))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x4 - x8) + sqr(x14 - x18) + sqr(x24
      - x28))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x4 - x9) + sqr(x14 - x19) + sqr(
     x24 - x29))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x4 - x10) + sqr(x14 - x20) + 
     sqr(x24 - x30))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x5 - x6) + sqr(x15 - x16)
      + sqr(x25 - x26))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x5 - x7) + sqr(x15 - 
     x17) + sqr(x25 - x27))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x5 - x8) + sqr(x15
      - x18) + sqr(x25 - x28))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x5 - x9) + sqr(
     x15 - x19) + sqr(x25 - x29))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x5 - x10) + 
     sqr(x15 - x20) + sqr(x25 - x30))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x6 - x7)
      + sqr(x16 - x17) + sqr(x26 - x27))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x6 - 
     x8) + sqr(x16 - x18) + sqr(x26 - x28))**0.5)) + sqr(1 - exp(3 - 3*(sqr(x6
      - x9) + sqr(x16 - x19) + sqr(x26 - x29))**0.5)) + sqr(1 - exp(3 - 3*(sqr(
     x6 - x10) + sqr(x16 - x20) + sqr(x26 - x30))**0.5)) + sqr(1 - exp(3 - 3*(
     sqr(x7 - x8) + sqr(x17 - x18) + sqr(x27 - x28))**0.5)) + sqr(1 - exp(3 - 3
     *(sqr(x7 - x9) + sqr(x17 - x19) + sqr(x27 - x29))**0.5)) + sqr(1 - exp(3
      - 3*(sqr(x7 - x10) + sqr(x17 - x20) + sqr(x27 - x30))**0.5)) + sqr(1 - 
     exp(3 - 3*(sqr(x8 - x9) + sqr(x18 - x19) + sqr(x28 - x29))**0.5)) + sqr(1
      - exp(3 - 3*(sqr(x8 - x10) + sqr(x18 - x20) + sqr(x28 - x30))**0.5)) + 
     sqr(1 - exp(3 - 3*(sqr(x9 - x10) + sqr(x19 - x20) + sqr(x29 - x30))**0.5))
     ) + objvar =E= -45;

* set non-default bounds
x1.fx = 0;
x2.lo = -5; x2.up = 5;
x3.lo = -5; x3.up = 5;
x4.lo = -5; x4.up = 5;
x5.lo = -5; x5.up = 5;
x6.lo = -5; x6.up = 5;
x7.lo = -5; x7.up = 5;
x8.lo = -5; x8.up = 5;
x9.lo = -5; x9.up = 5;
x10.lo = -5; x10.up = 5;
x11.fx = 0;
x12.fx = 0;
x13.lo = -5; x13.up = 5;
x14.lo = -5; x14.up = 5;
x15.lo = -5; x15.up = 5;
x16.lo = -5; x16.up = 5;
x17.lo = -5; x17.up = 5;
x18.lo = -5; x18.up = 5;
x19.lo = -5; x19.up = 5;
x20.lo = -5; x20.up = 5;
x21.fx = 0;
x22.fx = 0;
x23.fx = 0;
x24.lo = -5; x24.up = 5;
x25.lo = -5; x25.up = 5;
x26.lo = -5; x26.up = 5;
x27.lo = -5; x27.up = 5;
x28.lo = -5; x28.up = 5;
x29.lo = -5; x29.up = 5;
x30.lo = -5; x30.up = 5;

* set non-default levels
x2.l = 3.43266708;
x3.l = 0.50375356;
x4.l = -1.98862096;
x5.l = -2.07787883;
x6.l = -2.75947133;
x7.l = -1.50169496;
x8.l = 3.56270347;
x9.l = -4.32886277;
x10.l = 0.00210668999999974;
x13.l = 4.91133039;
x14.l = 2.62250467;
x15.l = -3.69307517;
x16.l = 1.39718759;
x17.l = -3.40482136;
x18.l = -2.49919467;
x19.l = 1.68928609;
x20.l = -0.64643619;
x24.l = -3.49898212;
x25.l = 0.8911365;
x26.l = 3.30892812;
x27.l = -2.69184262;
x28.l = 1.6573446;
x29.l = 2.75857606;
x30.l = -1.96341523;

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: 2018-09-14 Git hash: ac5a5314
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