MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance st_e25

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	0.89019359 p1 ( gdx sol ) (infeas: 4e-16)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	0.89019359 (ANTIGONE) 0.89019359 (BARON) 0.89019359 (COUENNE) 0.89019359 (CPLEX) 0.89019359 (GUROBI) 0.89019359 (LINDO) 0.89019352 (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. Thoai, N V, A global optimization approach for solving convex multiplicative programming problems, Journal of Global Optimization, 1:4, 1991, 341-357.
Sourceⓘ	BARON book instance misc/e25
Added to libraryⓘ	03 Sep 2002
Problem typeⓘ	QP
#Variablesⓘ	4
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	4
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	quadratic
Objective curvatureⓘ	indefinite
#Nonzeros in Objectiveⓘ	4
#Nonlinear Nonzeros in Objectiveⓘ	4
#Constraintsⓘ	8
#Linear Constraintsⓘ	8
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	linear
#Nonzeros in Jacobianⓘ	32
#Nonlinear Nonzeros in Jacobianⓘ	0
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	16
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	4
#Blocks in Hessian of Lagrangianⓘ	1
Minimal blocksize in Hessian of Lagrangianⓘ	4
Maximal blocksize in Hessian of Lagrangianⓘ	4
Average blocksize in Hessian of Lagrangianⓘ	4.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	6.0581e-02
Maximal coefficientⓘ	9.8309e-01
Infeasibility of initial pointⓘ	1.354
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          9        1        0        8        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          5        5        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         37       33        4        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,objvar;

Positive Variables  x1,x2,x3,x4;

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


e1..    0.488509*x1 + 0.063565*x2 + 0.945686*x3 + 0.210704*x4 =L= 3.562809;

e2..  - 0.324014*x1 - 0.501754*x2 - 0.719204*x3 + 0.099562*x4 =L= -0.052215;

e3..    0.445225*x1 - 0.346896*x2 + 0.637939*x3 - 0.257623*x4 =L= 0.42792;

e4..  - 0.202821*x1 + 0.647361*x2 + 0.920135*x3 + 0.983091*x4 =L= 0.84095;

e5..  - 0.88642*x1 - 0.802444*x2 - 0.305441*x3 - 0.180123*x4 =L= -1.353686;

e6..  - 0.515399*x1 - 0.42482*x2 + 0.897498*x3 + 0.187268*x4 =L= 2.137251;

e7..  - 0.591515*x1 + 0.060581*x2 - 0.427365*x3 + 0.579388*x4 =L= -0.290987;

e8..    0.423524*x1 + 0.940496*x2 - 0.437944*x3 - 0.742941*x4 =L= 0.37362;

e9.. -(0.217796 + 0.813396*x1 + 0.67444*x2 + 0.305038*x3 + 0.129742*x4)*(
     0.091947 + 0.224508*x1 + 0.063458*x2 + 0.93223*x3 + 0.528736*x4) + objvar
      =E= 0;

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;