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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex2_1_5

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-268.01463150 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-268.01463250 (ANTIGONE) -268.01463180 (BARON) -268.01463160 (COUENNE) -268.01463150 (CPLEX) -268.01463170 (GUROBI) -268.01463150 (LINDO) -268.01463860 (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 ex2.1.5 of Chapter 2 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	QP
#Variablesⓘ	10
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	7
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	quadratic
Objective curvatureⓘ	concave
#Nonzeros in Objectiveⓘ	10
#Nonlinear Nonzeros in Objectiveⓘ	7
#Constraintsⓘ	11
#Linear Constraintsⓘ	11
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	linear
#Nonzeros in Jacobianⓘ	101
#Nonlinear Nonzeros in Jacobianⓘ	0
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	7
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	7
#Blocks in Hessian of Lagrangianⓘ	7
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ⓘ	5.0000e-01
Maximal coefficientⓘ	9.0000e+01
Infeasibility of initial pointⓘ	6e-05
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         12        1        0       11        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         11       11        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        112      105        7        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,objvar;

Positive Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12;


e1.. -(-0.5*(10*x1*x1 + 10*x2*x2 + 10*x3*x3 + 10*x4*x4 + 10*x5*x5 + 10*x6*x6 + 
     10*x7*x7) - 20*x1 - 80*x2 - 20*x3 - 50*x4 - 60*x5 - 90*x6) - 10*x8 - 10*x9
      - 10*x10 + objvar =E= 0;

e2..  - 2*x1 - 6*x2 - x3 - 3*x5 - 3*x6 - 2*x7 - 6*x8 - 2*x9 - 2*x10 =L= -4;

e3..    6*x1 - 5*x2 + 8*x3 - 3*x4 + x6 + 3*x7 + 8*x8 + 9*x9 - 3*x10 =L= 22;

e4..  - 5*x1 + 6*x2 + 5*x3 + 3*x4 + 8*x5 - 8*x6 + 9*x7 + 2*x8 - 9*x10 =L= -6;

e5..    9*x1 + 5*x2 - 9*x4 + x5 - 8*x6 + 3*x7 - 9*x8 - 9*x9 - 3*x10 =L= -23;

e6..  - 8*x1 + 7*x2 - 4*x3 - 5*x4 - 9*x5 + x6 - 7*x7 - x8 + 3*x9 - 2*x10
      =L= -12;

e7..  - 7*x1 - 5*x2 - 2*x3 - 6*x5 - 6*x6 - 7*x7 - 6*x8 + 7*x9 + 7*x10 =L= -3;

e8..    x1 - 3*x2 - 3*x3 - 4*x4 - x5 - 4*x7 + x8 + 6*x9 =L= 1;

e9..    x1 - 2*x2 + 6*x3 + 9*x4 - 7*x6 + 9*x7 - 9*x8 - 6*x9 + 4*x10 =L= 12;

e10..  - 4*x1 + 6*x2 + 7*x3 + 2*x4 + 2*x5 + 6*x7 + 6*x8 - 7*x9 + 4*x10 =L= 15;

e11..    x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 =L= 9;

e12..  - x1 - x2 - x3 - x4 - x5 - x6 - x7 - x8 - x9 - x10 =L= -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;

* set non-default levels
x1.l = 1;
x2.l = 0.90755;
x4.l = 1;
x5.l = 0.71509;
x6.l = 1;
x8.l = 0.91698;
x9.l = 1;
x10.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;