MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

Home // Instances // Documentation // Download // Statistics

Instance st_e02

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	201.15933410 p1 ( gdx sol ) (infeas: 6e-14)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	201.15933390 (ANTIGONE) 201.15933370 (BARON) 201.15933390 (COUENNE) 201.15933410 (GUROBI) 201.15933410 (LINDO) 201.15933410 (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. Stoecker, W F, Design of Thermal Systems, McGraw Hill Book Co., New York, 1971.
Sourceⓘ	BARON book instance misc/e02
Added to libraryⓘ	03 Sep 2002
Problem typeⓘ	QCP
#Variablesⓘ	3
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	2
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	linear
Objective curvatureⓘ	linear
#Nonzeros in Objectiveⓘ	1
#Nonlinear Nonzeros in Objectiveⓘ	0
#Constraintsⓘ	3
#Linear Constraintsⓘ	0
#Quadratic Constraintsⓘ	3
#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ⓘ	2
#Blocks in Hessian of Lagrangianⓘ	1
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ⓘ	5.0000e-01
Maximal coefficientⓘ	3.0000e+01
Infeasibility of initial pointⓘ	300
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
*          4        4        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*          9        5        4        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,objvar;

Positive Variables  x1,x2,x3;

Equations  e1,e2,e3,e4;


e1.. 30*x1 - 6*x1*x1 - x3 =E= -250;

e2.. 20*x2 - 12*x2*x2 - x3 =E= -300;

e3.. 0.5*sqr(x1 + x2) - x3 =E= -150;

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

* set non-default bounds
x1.up = 9.422;
x2.up = 5.9023;
x3.up = 267.417085245;

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;