MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance st_e12

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	0.00000000 p1 ( gdx sol ) (infeas: 0) -4.51420165 p2 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-4.51420166 (ANTIGONE) -4.51420166 (BARON) -4.51420165 (COUENNE) -4.51420165 (LINDO) -4.51420165 (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. Stephanopoulos, G and Westerberg, A W, The use of Hestenes' method of multipliers to resolve dual gaps in engineering system optimization, Journal of Optimization Theory and Applications, 15:3, 1975, 285-309.
Sourceⓘ	BARON book instance misc/e12
Added to libraryⓘ	03 Sep 2002
Problem typeⓘ	NLP
#Variablesⓘ	4
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	2
#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ⓘ	2
#Constraintsⓘ	3
#Linear Constraintsⓘ	3
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	linear
#Nonzeros in Jacobianⓘ	7
#Nonlinear Nonzeros in Jacobianⓘ	0
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	2
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	2
#Blocks in Hessian of Lagrangianⓘ	2
Minimal blocksize in Hessian of Lagrangianⓘ	1
Maximal blocksize in Hessian of Lagrangianⓘ	1
Average blocksize in Hessian of Lagrangianⓘ	1.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	6.0000e-01
Maximal coefficientⓘ	6.0000e+00
Infeasibility of initial pointⓘ	0
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          4        2        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
*         12       10        2        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,objvar;

Positive Variables  x1,x2,x3,x4;

Equations  e1,e2,e3,e4;


e1..  - 3*x1 + x2 - 3*x3 =E= 0;

e2..    x1 + 2*x3 =L= 4;

e3..    x2 + 2*x4 =L= 4;

e4.. -(x1**0.6 + x2**0.6 - 6*x1) + 4*x3 - 3*x4 + objvar =E= 0;

* set non-default bounds
x1.up = 3;
x2.up = 4;
x3.up = 2;
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;