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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance st_e06

Formatsⓘ	ams gms mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	0.00000000 p1 ( gdx sol ) (infeas: 3e-10)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	0.00000000 (ANTIGONE) 0.00000000 (BARON) 0.00000000 (COUENNE) 0.00000000 (LINDO) 0.00000000 (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. Liebman, J, Lasdon, L S, Schrage, L, and Waren, A D, Modeling and Optimization with GINO, The Scientific Press, Palo Alto, CA, 1986.
Sourceⓘ	BARON book instance misc/e06
Added to libraryⓘ	03 Sep 2002
Problem typeⓘ	NLP
#Variablesⓘ	3
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	3
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	constant
Objective curvatureⓘ	linear
#Nonzeros in Objectiveⓘ	0
#Nonlinear Nonzeros in Objectiveⓘ	0
#Constraintsⓘ	3
#Linear Constraintsⓘ	2
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	1
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	8
#Nonlinear Nonzeros in Jacobianⓘ	3
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	4
#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ⓘ	2
Average blocksize in Hessian of Lagrangianⓘ	1.5
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	1.6900e-04
Maximal coefficientⓘ	3.0000e+00
Infeasibility of initial pointⓘ	50
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        6        3        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,objvar;

Positive Variables  x1,x2,x3;

Equations  e1,e2,e3,e4;


e1.. x3*x3 - 0.000169*POWER(x2,3)*x1 =E= 0;

e2..    x1 + x2 + x3 =E= 50;

e3..  - 3*x1 + x2 =E= 0;

e4..    objvar =E= 0;

* set non-default bounds
x1.up = 12.5;
x2.up = 37.5;
x3.up = 50;

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;