MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance st_e21

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-13.40190356 p2 ( gdx sol ) (infeas: 0) 0. p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-13.40190357 (ANTIGONE) -13.40190358 (BARON) -13.40190356 (COUENNE) -13.40190356 (LINDO) -13.40190356 (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/e21
Added to libraryⓘ	03 Sep 2002
Problem typeⓘ	NLP
#Variablesⓘ	6
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	3
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	signomial
Objective curvatureⓘ	concave
#Nonzeros in Objectiveⓘ	6
#Nonlinear Nonzeros in Objectiveⓘ	3
#Constraintsⓘ	6
#Linear Constraintsⓘ	6
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	linear
#Nonzeros in Jacobianⓘ	14
#Nonlinear Nonzeros in Jacobianⓘ	0
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	3
#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ⓘ	1
Average blocksize in Hessian of Lagrangianⓘ	1.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	4.0000e-01
Maximal coefficientⓘ	5.0000e+00
Infeasibility of initial pointⓘ	0
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          7        4        0        3        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          7        7        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         21       18        3        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,objvar;

Positive Variables  x1,x2,x3,x4,x5,x6;

Equations  e1,e2,e3,e4,e5,e6,e7;


e1..  - 3*x1 + x2 - 3*x4 =E= 0;

e2..  - 2*x2 + x3 - 2*x5 =E= 0;

e3..    4*x4 - x6 =E= 0;

e4..    x1 + 2*x4 =L= 4;

e5..    x2 + x5 =L= 4;

e6..    x3 + x6 =L= 6;

e7.. -(x1**0.6 + x2**0.6 + x3**0.4 - 4*x3) - 2*x4 - 5*x5 + x6 + objvar =E= 0;

* set non-default bounds
x1.up = 3;
x2.up = 4;
x3.up = 4;
x4.up = 2;
x5.up = 2;
x6.up = 6;

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;