MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance st_e05

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	7049.24927200 p1 ( gdx sol ) (infeas: 4e-09)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	7049.24926500 (ANTIGONE) 7049.24926500 (BARON) 7049.24927200 (COUENNE) 7049.24927200 (GUROBI) 7049.24927200 (LINDO) 7049.24927200 (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. Liebman, J, Lasdon, L S, Schrage, L, and Waren, A D, Modeling and Optimization with GINO, The Scientific Press, Palo Alto, CA, 1986.
Sourceⓘ	BARON book instance misc/e05
Added to libraryⓘ	03 Sep 2002
Problem typeⓘ	QCP
#Variablesⓘ	5
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	4
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	linear
Objective curvatureⓘ	linear
#Nonzeros in Objectiveⓘ	3
#Nonlinear Nonzeros in Objectiveⓘ	0
#Constraintsⓘ	3
#Linear Constraintsⓘ	1
#Quadratic Constraintsⓘ	2
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	7
#Nonlinear Nonzeros in Jacobianⓘ	4
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	4
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	0
#Blocks in Hessian of Lagrangianⓘ	2
Minimal blocksize in Hessian of Lagrangianⓘ	2
Maximal blocksize in Hessian of Lagrangianⓘ	2
Average blocksize in Hessian of Lagrangianⓘ	2.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	1.0000e+00
Maximal coefficientⓘ	1.0000e+05
Infeasibility of initial pointⓘ	4e+07
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          4        4        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          6        6        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         11        7        4        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,objvar;

Positive Variables  x1,x2,x3;

Equations  e1,e2,e3,e4;


e1.. 100000*x4 - 120*x1*(300 - x4) =E= 10000000;

e2.. 100000*x5 - 80*x2*(400 - x5) - 100000*x4 =E= 0;

e3..  - 4000*x3 - 100000*x5 =E= -50000000;

e4..  - x1 - x2 - x3 + objvar =E= 0;

* set non-default bounds
x1.up = 15834;
x2.up = 36250;
x3.up = 10000;
x4.lo = 100; x4.up = 300;
x5.lo = 100; x5.up = 400;

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;