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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex2_1_8

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	25287.00000000 p1 ( gdx sol ) (infeas: 0) 15639.00000000 p2 ( gdx sol ) (infeas: 3e-10)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	15638.99998000 (ANTIGONE) 15638.99998000 (BARON) 15639.00000000 (COUENNE) 15639.00000000 (CPLEX) 15639.00000000 (GUROBI) 15639.00000000 (LINDO) 15638.99991000 (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 ex2.1.8 of Chapter 2 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	QP
#Variablesⓘ	24
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	24
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	quadratic
Objective curvatureⓘ	concave
#Nonzeros in Objectiveⓘ	24
#Nonlinear Nonzeros in Objectiveⓘ	24
#Constraintsⓘ	10
#Linear Constraintsⓘ	10
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	linear
#Nonzeros in Jacobianⓘ	48
#Nonlinear Nonzeros in Jacobianⓘ	0
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	24
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	24
#Blocks in Hessian of Lagrangianⓘ	24
Minimal blocksize in Hessian of Lagrangianⓘ	1
Maximal blocksize in Hessian of Lagrangianⓘ	1
Average blocksize in Hessian of Lagrangianⓘ	1.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	1.0000e+00
Maximal coefficientⓘ	8.3000e+02
Infeasibility of initial pointⓘ	24
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         11       11        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         25       25        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         73       49       24        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,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;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11;


e1.. -(300*x1 - 7*x1*x1 - 4*x2*x2 + 270*x2 - 6*x3*x3 + 460*x3 - 8*x4*x4 + 800*
     x4 - 12*x5*x5 + 740*x5 - 9*x6*x6 + 600*x6 - 14*x7*x7 + 540*x7 - 7*x8*x8 + 
     380*x8 - 13*x9*x9 + 300*x9 - 12*x10*x10 + 490*x10 - 8*x11*x11 + 380*x11 - 
     4*x12*x12 + 760*x12 - 7*x13*x13 + 430*x13 - 9*x14*x14 + 250*x14 - 16*x15*
     x15 + 390*x15 - 8*x16*x16 + 600*x16 - 4*x17*x17 + 210*x17 - 10*x18*x18 + 
     830*x18 - 21*x19*x19 + 470*x19 - 13*x20*x20 + 680*x20 - 17*x21*x21 + 360*
     x21 - 9*x22*x22 + 290*x22 - 8*x23*x23 + 400*x23 - 4*x24*x24 + 310*x24)
      + objvar =E= 0;

e2..    x1 + x2 + x3 + x4 =E= 8;

e3..    x5 + x6 + x7 + x8 =E= 24;

e4..    x9 + x10 + x11 + x12 =E= 20;

e5..    x13 + x14 + x15 + x16 =E= 24;

e6..    x17 + x18 + x19 + x20 =E= 16;

e7..    x21 + x22 + x23 + x24 =E= 12;

e8..    x1 + x5 + x9 + x13 + x17 + x21 =E= 29;

e9..    x2 + x6 + x10 + x14 + x18 + x22 =E= 41;

e10..    x3 + x7 + x11 + x15 + x19 + x23 =E= 13;

e11..    x4 + x8 + x12 + x16 + x20 + x24 =E= 21;

* set non-default bounds
x1.up = 100;
x2.up = 100;
x3.up = 100;
x4.up = 100;
x5.up = 100;
x6.up = 100;
x7.up = 100;
x8.up = 100;
x9.up = 100;
x10.up = 100;
x11.up = 100;
x12.up = 100;
x13.up = 100;
x14.up = 100;
x15.up = 100;
x16.up = 100;
x17.up = 100;
x18.up = 100;
x19.up = 100;
x20.up = 100;
x21.up = 100;
x22.up = 100;
x23.up = 100;
x24.up = 100;

* set non-default levels
x1.l = 6;
x2.l = 2;
x6.l = 3;
x8.l = 21;
x9.l = 20;
x13.l = 24;
x17.l = 3;
x19.l = 13;
x22.l = 12;

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;