MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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

Instance st_e04

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	5194.866244 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	5194.866239 (ANTIGONE) 5194.866239 (BARON) 5194.866244 (COUENNE) 5194.866244 (LINDO) 5194.866244 (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/e04
Added to libraryⓘ	03 Sep 2002
Problem typeⓘ	NLP
#Variablesⓘ	4
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	4
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	nonlinear
Objective curvatureⓘ	indefinite
#Nonzeros in Objectiveⓘ	3
#Nonlinear Nonzeros in Objectiveⓘ	2
#Constraintsⓘ	2
#Linear Constraintsⓘ	0
#Quadratic Constraintsⓘ	1
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	1
Operands in Gen. Nonlin. Functionsⓘ	div exp vcpower
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	5
#Nonlinear Nonzeros in Jacobianⓘ	3
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	5
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	3
#Blocks in Hessian of Lagrangianⓘ	3
Minimal blocksize in Hessian of Lagrangianⓘ	1
Maximal blocksize in Hessian of Lagrangianⓘ	2
Average blocksize in Hessian of Lagrangianⓘ	1.333333
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	9.0000e-01
Maximal coefficientⓘ	3.9500e+03
Infeasibility of initial pointⓘ	1.152e+04
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          3        2        1        0        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
*          9        4        5        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,objvar;

Positive Variables  x1,x3;

Equations  e1,e2,e3;


e1.. x3*x1 + 144*x4 =G= 11520;

e2.. -exp(11.86 - 3950/(460 + x4)) + x2 =E= 0;

e3.. -(400*x1**0.9 + 22*(-14.7 + x2)**1.2) - x3 + objvar =E= 1000;

* set non-default bounds
x1.up = 15.1;
x2.lo = 14.7; x2.up = 94.2;
x3.up = 5371;
x4.lo = -459.67; x4.up = 80;

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;