MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex5_2_2_case1

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-0.00000000 p1 ( gdx sol ) (infeas: 0) -100.00000000 p2 ( gdx sol ) (infeas: 3e-14) -400.00000000 p3 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-400.00000040 (ANTIGONE) -400.00000040 (BARON) -400.00000000 (COUENNE) -400.00000000 (GUROBI) -400.00000000 (LINDO) -400.00000190 (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. Haverly, C A, Studies of the Behavior of Recursion for the Pooling Problem, ACM SIGMAP Bull, 25, 1978, 19-28.
Sourceⓘ	Test Problem ex5.2.2_case1 of Chapter 5 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	QCP
#Variablesⓘ	9
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	3
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	linear
Objective curvatureⓘ	linear
#Nonzeros in Objectiveⓘ	6
#Nonlinear Nonzeros in Objectiveⓘ	0
#Constraintsⓘ	6
#Linear Constraintsⓘ	3
#Quadratic Constraintsⓘ	3
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	23
#Nonlinear Nonzeros in Jacobianⓘ	7
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	4
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	0
#Blocks in Hessian of Lagrangianⓘ	1
Minimal blocksize in Hessian of Lagrangianⓘ	3
Maximal blocksize in Hessian of Lagrangianⓘ	3
Average blocksize in Hessian of Lagrangianⓘ	3.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	1.0000e+00
Maximal coefficientⓘ	1.6000e+01
Infeasibility of initial pointⓘ	0
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          7        5        0        2        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         10       10        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         30       23        7        0
*
*  Solve m using NLP minimizing objvar;


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

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

Equations  e1,e2,e3,e4,e5,e6,e7;


e1..  - 9*x1 - 15*x2 + 6*x3 + 16*x4 + 10*x5 + 10*x6 - objvar =E= 0;

e2..  - x3 - x4 + x8 + x9 =E= 0;

e3..    x1 - x5 - x8 =E= 0;

e4..    x2 - x6 - x9 =E= 0;

e5.. x7*x8 - 2.5*x1 + 2*x5 =L= 0;

e6.. x7*x9 - 1.5*x2 + 2*x6 =L= 0;

e7.. x7*x8 + x7*x9 - 3*x3 - x4 =E= 0;

* set non-default bounds
x1.up = 100;
x2.up = 200;
x3.up = 500;
x4.up = 500;
x5.up = 500;
x6.up = 500;
x7.up = 500;
x8.up = 500;
x9.up = 500;

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;