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Instance: ex8_3_9

Formats ams gms lp mod nl osil pip
Primal Bounds
-0.74161985 p1 ( gdx sol )
(infeas: 3e-14)
-0.76300193 p2 ( gdx sol )
(infeas: 3e-13)
Dual Bounds
-1.00000025 (ANTIGONE)
-1.00000000 (BARON)
-10.00000000 (COUENNE)
-10.00000000 (LINDO)
-10.00000000 (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 ex8.3.9 of Chapter 8 of Floudas e.a. handbook
Added to library 31 Jul 2001
Problem type QCP
#Variables 78
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 73
#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 45
#Linear Constraints 18
#Quadratic Constraints 27
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 325
#Nonlinear Nonzeros in Jacobian 214
#Nonzeros in (Upper-Left) Hessian of Lagrangian 184
#Nonzeros in Diagonal of Hessian of Lagrangian 0
#Blocks in Hessian of Lagrangian 16
Minimal blocksize in Hessian of Lagrangian 2
Maximal blocksize in Hessian of Lagrangian 9
Average blocksize in Hessian of Lagrangian 4.5625
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Infeasibility of initial point 250
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
*         46       46        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         79       79        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        327      113      214        0
*
*  Solve m using NLP minimizing objvar;


Variables  objvar,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,x63,x64,x65,x66,x67,x68,x69
          ,x70,x71,x72,x73,x74,x75,x76,x77,x78,x79;

Positive Variables  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,x63,x64,x65,x66,x67,x68
          ,x69,x70,x71,x72,x73,x74,x75,x76,x77,x78,x79;

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;


e1..  - objvar - x69 =E= 0;

e2..  - x2 - x3 - x4 - x5 - x6 =E= -100;

e3..  - x2 + x7 - x37 - x42 - x47 - x52 - x57 =E= 0;

e4..  - x3 + x8 - x38 - x43 - x48 - x53 - x58 =E= 0;

e5..  - x4 + x9 - x39 - x44 - x49 - x54 - x59 =E= 0;

e6..  - x5 + x10 - x40 - x45 - x50 - x55 - x60 =E= 0;

e7..  - x6 + x11 - x41 - x46 - x51 - x56 - x61 =E= 0;

e8.. x12*x7 - (x27*x37 + x29*x42 + x31*x47 + x33*x52 + x35*x57) - 0.45*x2 =E= 0
     ;

e9.. x13*x7 - (x28*x37 + x30*x42 + x32*x47 + x34*x52 + x36*x57) - 0.55*x2 =E= 0
     ;

e10.. x14*x8 - (x27*x38 + x29*x43 + x31*x48 + x33*x53 + x35*x58) - 0.45*x3
       =E= 0;

e11.. x15*x8 - (x28*x38 + x30*x43 + x32*x48 + x34*x53 + x36*x58) - 0.55*x3
       =E= 0;

e12.. x16*x9 - (x27*x39 + x29*x44 + x31*x49 + x33*x54 + x35*x59) - 0.45*x4
       =E= 0;

e13.. x17*x9 - (x28*x39 + x30*x44 + x32*x49 + x34*x54 + x36*x59) - 0.55*x4
       =E= 0;

e14.. x18*x10 - (x27*x40 + x29*x45 + x31*x50 + x33*x55 + x35*x60) - 0.45*x5
       =E= 0;

e15.. x19*x10 - (x28*x40 + x30*x45 + x32*x50 + x34*x55 + x36*x60) - 0.55*x5
       =E= 0;

e16.. x20*x11 - (x27*x41 + x29*x46 + x31*x51 + x33*x56 + x35*x61) - 0.45*x6
       =E= 0;

e17.. x21*x11 - (x28*x41 + x30*x46 + x32*x51 + x34*x56 + x36*x61) - 0.55*x6
       =E= 0;

e18..  - x7 + x22 =E= 0;

e19..  - x8 + x23 =E= 0;

e20..  - x9 + x24 =E= 0;

e21..  - x10 + x25 =E= 0;

e22..  - x11 + x26 =E= 0;

e23.. x27*x22 - (x12*x7 - x70*x75) =E= 0;

e24.. x28*x22 - (x13*x7 + x70*x75) =E= 0;

e25.. x29*x23 - (x14*x8 - x71*x76) =E= 0;

e26.. x30*x23 - (x15*x8 + x71*x76) =E= 0;

e27.. x31*x24 - (x16*x9 - x72*x77) =E= 0;

e28.. x32*x24 - (x17*x9 + x72*x77) =E= 0;

e29.. x33*x25 - (x18*x10 - x73*x78) =E= 0;

e30.. x34*x25 - (x19*x10 + x73*x78) =E= 0;

e31.. x35*x26 - (x20*x11 - x74*x79) =E= 0;

e32.. x36*x26 - (x21*x11 + x74*x79) =E= 0;

e33.. -x27*x28 + x75 =E= 0;

e34.. -x29*x30 + x76 =E= 0;

e35.. -x31*x32 + x77 =E= 0;

e36.. -x33*x34 + x78 =E= 0;

e37.. -x35*x36 + x79 =E= 0;

e38..    x22 - x37 - x38 - x39 - x40 - x41 - x62 =E= 0;

e39..    x23 - x42 - x43 - x44 - x45 - x46 - x63 =E= 0;

e40..    x24 - x47 - x48 - x49 - x50 - x51 - x64 =E= 0;

e41..    x25 - x52 - x53 - x54 - x55 - x56 - x65 =E= 0;

e42..    x26 - x57 - x58 - x59 - x60 - x61 - x66 =E= 0;

e43..  - x62 - x63 - x64 - x65 - x66 + x67 =E= 0;

e44.. x67*x68 - (x62*x27 + x63*x29 + x64*x31 + x65*x33 + x66*x35) =E= 0;

e45.. x67*x69 - (x62*x28 + x63*x30 + x64*x32 + x65*x34 + x66*x36) =E= 0;

e46..    x70 + x71 + x72 + x73 + x74 =E= 100;

* set non-default bounds
x2.up = 1000;
x3.up = 1000;
x4.up = 1000;
x5.up = 1000;
x6.up = 1000;
x7.up = 1000;
x8.up = 1000;
x9.up = 1000;
x10.up = 1000;
x11.up = 1000;
x12.up = 10;
x13.up = 10;
x14.up = 10;
x15.up = 10;
x16.up = 10;
x17.up = 10;
x18.up = 10;
x19.up = 10;
x20.up = 10;
x21.up = 10;
x22.up = 1000;
x23.up = 1000;
x24.up = 1000;
x25.up = 1000;
x26.up = 1000;
x27.up = 10;
x28.up = 10;
x29.up = 10;
x30.up = 10;
x31.up = 10;
x32.up = 10;
x33.up = 10;
x34.up = 10;
x35.up = 10;
x36.up = 10;
x37.up = 1000;
x38.up = 1000;
x39.up = 1000;
x40.up = 1000;
x41.up = 1000;
x42.up = 1000;
x43.up = 1000;
x44.up = 1000;
x45.up = 1000;
x46.up = 1000;
x47.up = 1000;
x48.up = 1000;
x49.up = 1000;
x50.up = 1000;
x51.up = 1000;
x52.up = 1000;
x53.up = 1000;
x54.up = 1000;
x55.up = 1000;
x56.up = 1000;
x57.up = 1000;
x58.up = 1000;
x59.up = 1000;
x60.up = 1000;
x61.up = 1000;
x62.up = 1000;
x63.up = 1000;
x64.up = 1000;
x65.up = 1000;
x66.up = 1000;
x67.up = 1000;
x68.up = 10;
x69.up = 10;
x70.up = 10000;
x71.up = 10000;
x72.up = 10000;
x73.up = 10000;
x74.up = 10000;
x75.up = 10000;
x76.up = 10000;
x77.up = 10000;
x78.up = 10000;
x79.up = 10000;

* set non-default levels
x2.l = 50;
x3.l = 50;
x4.l = 50;
x5.l = 50;
x6.l = 50;
x7.l = 50;
x8.l = 50;
x9.l = 50;
x10.l = 50;
x11.l = 50;
x12.l = 0.2;
x13.l = 0.2;
x14.l = 0.2;
x15.l = 0.2;
x16.l = 0.2;
x17.l = 0.2;
x18.l = 0.2;
x19.l = 0.2;
x20.l = 0.2;
x21.l = 0.2;
x22.l = 100;
x23.l = 100;
x24.l = 100;
x25.l = 100;
x26.l = 100;
x27.l = 0.2;
x28.l = 0.2;
x29.l = 0.2;
x30.l = 0.2;
x31.l = 0.2;
x32.l = 0.2;
x33.l = 0.2;
x34.l = 0.2;
x35.l = 0.2;
x36.l = 0.2;
x37.l = 50;
x38.l = 50;
x39.l = 50;
x40.l = 50;
x41.l = 50;
x42.l = 50;
x43.l = 50;
x44.l = 50;
x45.l = 50;
x46.l = 50;
x47.l = 50;
x48.l = 50;
x49.l = 50;
x50.l = 50;
x51.l = 50;
x52.l = 50;
x53.l = 50;
x54.l = 50;
x55.l = 50;
x56.l = 50;
x57.l = 50;
x58.l = 50;
x59.l = 50;
x60.l = 50;
x61.l = 50;
x62.l = 50;
x63.l = 50;
x64.l = 50;
x65.l = 50;
x66.l = 50;
x67.l = 100;
x68.l = 0.2;
x69.l = 0.2;
x70.l = 1;
x71.l = 1;
x72.l = 1;
x73.l = 1;
x74.l = 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: 2018-09-14 Git hash: ac5a5314
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