MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance st_e13

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	2.00000000 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	2.00000000 (ANTIGONE) 2.00000000 (BARON) 2.00000000 (COUENNE) 2.00000000 (GUROBI) 2.00000000 (LINDO) 2.00000000 (SCIP) 0.00000000 (SHOT)
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. Kocis, Gary R and Grossmann, I E, Global Optimization of Nonconvex MINLP Problems in Process Synthesis, Industrial and Engineering Chemistry Research, 27:8, 1988, 1407-1421.
Sourceⓘ	BARON book instance misc/e13
Added to libraryⓘ	01 Sep 2002
Problem typeⓘ	MBQCP
#Variablesⓘ	2
#Binary Variablesⓘ	1
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	1
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	linear
Objective curvatureⓘ	linear
#Nonzeros in Objectiveⓘ	2
#Nonlinear Nonzeros in Objectiveⓘ	0
#Constraintsⓘ	2
#Linear Constraintsⓘ	1
#Quadratic Constraintsⓘ	1
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	concave
#Nonzeros in Jacobianⓘ	4
#Nonlinear Nonzeros in Jacobianⓘ	1
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	1
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	1
#Blocks in Hessian of Lagrangianⓘ	1
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ⓘ	1.0000e+00
Maximal coefficientⓘ	2.0000e+00
Infeasibility of initial pointⓘ	1.25
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
*          3        2        1        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*          7        6        1        0
*
*  Solve m using MINLP minimizing objvar;


Variables  b1,x2,objvar;

Positive Variables  x2;

Binary Variables  b1;

Equations  e1,e2,e3;


e1.. -sqr(x2) - b1 =L= -1.25;

e2..    b1 + x2 =L= 1.6;

e3..  - b1 - 2*x2 + objvar =E= 0;

* set non-default bounds
x2.up = 1.6;

Model m / all /;

m.limrow=0; m.limcol=0;
m.tolproj=0.0;

$if NOT '%gams.u1%' == '' $include '%gams.u1%'

$if not set MINLP $set MINLP MINLP
Solve m using %MINLP% minimizing objvar;