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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance st_e41

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	641.82356230 p1 ( gdx sol ) (infeas: 2e-15)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	641.82356170 (ANTIGONE) 641.82356100 (BARON) 641.82315590 (COUENNE) 641.82345950 (LINDO) 641.82355980 (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. Kim, Y S, Problems in reliability, 1998. Personal Communication.
Sourceⓘ	BARON book instance misc/e41
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ⓘ	signomial
Objective curvatureⓘ	concave
#Nonzeros in Objectiveⓘ	4
#Nonlinear Nonzeros in Objectiveⓘ	4
#Constraintsⓘ	2
#Linear Constraintsⓘ	0
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	2
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	8
#Nonlinear Nonzeros in Jacobianⓘ	8
#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ⓘ	6.0000e-01
Maximal coefficientⓘ	3.0000e+02
Infeasibility of initial pointⓘ	0.1266
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          3        1        0        2        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
*         13        1       12        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,objvar;

Equations  e1,e2,e3;


e1.. -(-sqr(1 - x1)*x3*sqr(1 - x4) - sqr(1 - (1 - (1 - x1)*(1 - x4))*x2)*(1 - 
     x3)) =L= 0.1;

e2.. (-sqr(1 - x1)*x3*sqr(1 - x4)) - sqr(1 - (1 - (1 - x1)*(1 - x4))*x2)*(1 - 
     x3) =L= 0;

e3.. -(200*x1**0.6 + 200*x2**0.6 + 200*x3**0.6 + 300*x4**0.6) + objvar =E= 0;

* set non-default bounds
x1.lo = 0.5; x1.up = 1;
x2.lo = 0.5; x2.up = 1;
x3.lo = 0.5; x3.up = 1;
x4.lo = 0.5; x4.up = 1;

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;