MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance st_e33

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-400.00000000 p1 ( gdx sol ) (infeas: 3e-14)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-400.00000040 (ANTIGONE) -400.00000040 (BARON) -400.00000000 (COUENNE) -400.00000000 (GUROBI) -400.00000000 (LINDO) -400.00000000 (SCIP)
Referencesⓘ	Tawarmalani, M and Sahinidis, N V, Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications, Kluwer, 2002. Xia, Q, A constrained problem difficult for genetic algorithms, 1996.
Sourceⓘ	BARON book instance misc/e33
Added to libraryⓘ	03 Sep 2002
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-02
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;

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


e1..    x1 + x2 - x3 - x4 =E= 0;

e2.. -x9*(x3 + x4) + 0.03*x1 + 0.01*x2 =E= 0;

e3..    x3 - x5 + x6 =E= 0;

e4..    x4 + x7 - x8 =E= 0;

e5.. x9*x3 - 0.025*x5 + 0.02*x6 =L= 0;

e6.. x9*x4 + 0.02*x7 - 0.015*x8 =L= 0;

e7..  - 6*x1 - 16*x2 + 9*x5 - 10*x6 - 10*x7 + 15*x8 + objvar =E= 0;

* set non-default bounds
x1.up = 300;
x2.up = 300;
x3.up = 100;
x4.up = 200;
x5.up = 100;
x6.up = 300;
x7.up = 100;
x8.up = 200;
x9.lo = 0.01; x9.up = 0.03;

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;