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Instance ex5_2_5

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-3500.00000000 p1 ( gdx sol ) (infeas: 6e-11)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-3500.00000400 (ANTIGONE) -5490.68447400 (BARON) -6984.32764400 (COUENNE) -3500.00000000 (GUROBI) -6409.96849000 (LINDO) -3709.46379800 (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. Ben-Tal, A, Eiger, G, and Gershovitz, V, Global Minimization by Reducing the Duality Gap, Mathematical Programming, 63:1, 1994, 193-212.
Sourceⓘ	Test Problem ex5.2.5 of Chapter 5 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	QCQP
#Variablesⓘ	32
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	27
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	quadratic
Objective curvatureⓘ	indefinite
#Nonzeros in Objectiveⓘ	32
#Nonlinear Nonzeros in Objectiveⓘ	27
#Constraintsⓘ	19
#Linear Constraintsⓘ	8
#Quadratic Constraintsⓘ	11
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	206
#Nonlinear Nonzeros in Jacobianⓘ	168
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	120
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	0
#Blocks in Hessian of Lagrangianⓘ	3
Minimal blocksize in Hessian of Lagrangianⓘ	9
Maximal blocksize in Hessian of Lagrangianⓘ	9
Average blocksize in Hessian of Lagrangianⓘ	9.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	1.0000e-01
Maximal coefficientⓘ	1.9000e+01
Infeasibility of initial pointⓘ	1
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         20        4        0       16        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         33       33        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        239       44      195        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,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;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19
          ,e20;


e1.. -((18 - 6*x1 - 16*x4 - 15*x7 - 12*x10)*x18 + (18 - 6*x2 - 16*x5 - 15*x8 - 
     12*x11)*x23 + (18 - 6*x3 - 16*x6 - 15*x9 - 12*x12)*x28 + (15 - 6*x1 - 16*
     x4 - 15*x7 - 12*x10)*x19 + (15 - 6*x2 - 16*x5 - 15*x8 - 12*x11)*x24 + (15
      - 6*x3 - 16*x6 - 15*x9 - 12*x12)*x29 + (19 - 6*x1 - 16*x4 - 15*x7 - 12*
     x10)*x20 + (19 - 6*x2 - 16*x5 - 15*x8 - 12*x11)*x25 + (19 - 6*x3 - 16*x6
      - 15*x9 - 12*x12)*x30 + (16 - 6*x1 - 16*x4 - 15*x7 - 12*x10)*x21 + (16 - 
     6*x2 - 16*x5 - 15*x8 - 12*x11)*x26 + (16 - 6*x3 - 16*x6 - 15*x9 - 12*x12)*
     x31 + (14 - 6*x1 - 16*x4 - 15*x7 - 12*x10)*x22 + (14 - 6*x2 - 16*x5 - 15*
     x8 - 12*x11)*x27 + (14 - 6*x3 - 16*x6 - 15*x9 - 12*x12)*x32) - 8*x13
      - 5*x14 - 9*x15 - 6*x16 - 4*x17 - objvar =E= 0;

e2.. x7*x18 + x7*x19 + x7*x20 + x7*x21 + x7*x22 + x8*x23 + x8*x24 + x8*x25 + x8
     *x26 + x8*x27 + x9*x28 + x9*x29 + x9*x30 + x9*x31 + x9*x32 =L= 50;

e3..    x13 + x18 + x23 + x28 =L= 100;

e4..    x14 + x19 + x24 + x29 =L= 200;

e5..    x15 + x20 + x25 + x30 =L= 100;

e6..    x16 + x21 + x26 + x31 =L= 100;

e7..    x17 + x22 + x27 + x32 =L= 100;

e8.. (-2.5 + 3*x1 + x4 + x7 + 1.5*x10)*x18 + (-2.5 + 3*x2 + x5 + x8 + 1.5*x11)*
     x23 + (-2.5 + 3*x3 + x6 + x9 + 1.5*x12)*x28 - 0.5*x13 =L= 0;

e9.. (-2 + x1 + 3*x4 + 2.5*x7 + 2.5*x10)*x18 + (-2 + x2 + 3*x5 + 2.5*x8 + 2.5*
     x11)*x23 + (-2 + x3 + 3*x6 + 2.5*x9 + 2.5*x12)*x28 + 0.5*x13 =L= 0;

e10.. (-1.5 + 3*x1 + x4 + x7 + 1.5*x10)*x19 + (-1.5 + 3*x2 + x5 + x8 + 1.5*x11)
      *x24 + (-1.5 + 3*x3 + x6 + x9 + 1.5*x12)*x29 + 0.5*x14 =L= 0;

e11.. (-2.5 + x1 + 3*x4 + 2.5*x7 + 2.5*x10)*x19 + (-2.5 + x2 + 3*x5 + 2.5*x8 + 
      2.5*x11)*x24 + (-2.5 + x3 + 3*x6 + 2.5*x9 + 2.5*x12)*x29 =L= 0;

e12.. (-2 + 3*x1 + x4 + x7 + 1.5*x10)*x20 + (-2 + 3*x2 + x5 + x8 + 1.5*x11)*x25
       + (-2 + 3*x3 + x6 + x9 + 1.5*x12)*x30 =L= 0;

e13.. (-2.6 + x1 + 3*x4 + 2.5*x7 + 2.5*x10)*x20 + (-2.6 + x2 + 3*x5 + 2.5*x8 + 
      2.5*x11)*x25 + (-2.6 + x3 + 3*x6 + 2.5*x9 + 2.5*x12)*x30 - 0.1*x15 =L= 0;

e14.. (-2 + 3*x1 + x4 + x7 + 1.5*x10)*x21 + (-2 + 3*x2 + x5 + x8 + 1.5*x11)*x26
       + (-2 + 3*x3 + x6 + x9 + 1.5*x12)*x31 =L= 0;

e15.. (-2 + x1 + 3*x4 + 2.5*x7 + 2.5*x10)*x21 + (-2 + x2 + 3*x5 + 2.5*x8 + 2.5*
      x11)*x26 + (-2 + x3 + 3*x6 + 2.5*x9 + 2.5*x12)*x31 + 0.5*x16 =L= 0;

e16.. (-2 + 3*x1 + x4 + x7 + 1.5*x10)*x22 + (-2 + 3*x2 + x5 + x8 + 1.5*x11)*x27
       + (-2 + 3*x3 + x6 + x9 + 1.5*x12)*x32 =L= 0;

e17.. (-2 + x1 + 3*x4 + 2.5*x7 + 2.5*x10)*x22 + (-2 + x2 + 3*x5 + 2.5*x8 + 2.5*
      x11)*x27 + (-2 + x3 + 3*x6 + 2.5*x9 + 2.5*x12)*x32 + 0.5*x17 =L= 0;

e18..    x1 + x4 + x7 + x10 =E= 1;

e19..    x2 + x5 + x8 + x11 =E= 1;

e20..    x3 + x6 + x9 + x12 =E= 1;

* set non-default bounds
x1.up = 1;
x2.up = 1;
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 = 100;
x14.up = 200;
x15.up = 100;
x16.up = 100;
x17.up = 100;
x18.up = 100;
x19.up = 200;
x20.up = 100;
x21.up = 100;
x22.up = 100;
x23.up = 100;
x24.up = 200;
x25.up = 100;
x26.up = 100;
x27.up = 100;
x28.up = 100;
x29.up = 200;
x30.up = 100;
x31.up = 100;
x32.up = 100;

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;