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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance st_e36

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-246. p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-246. (ANTIGONE) -246. (BARON) -246. (COUENNE) -246. (LINDO) -246. (SCIP) -275. (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. Li, Han-Lin and Chou, Chih-Tan, A global approach for nonlinear mixed discrete programming in design optimization, Engineering Optimization, 22:2, 1994, 109-122.
Sourceⓘ	BARON book instance misc/e36
Added to libraryⓘ	01 Sep 2002
Problem typeⓘ	MINLP
#Variablesⓘ	2
#Binary Variablesⓘ	0
#Integer Variablesⓘ	1
#Nonlinear Variablesⓘ	2
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	1
Objective Senseⓘ	min
Objective typeⓘ	polynomial
Objective curvatureⓘ	nonconcave
#Nonzeros in Objectiveⓘ	2
#Nonlinear Nonzeros in Objectiveⓘ	2
#Constraintsⓘ	2
#Linear Constraintsⓘ	0
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	1
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	1
Operands in Gen. Nonlin. Functionsⓘ	exp mul
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	4
#Nonlinear Nonzeros in Jacobianⓘ	4
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	4
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	2
#Blocks in Hessian of Lagrangianⓘ	1
Minimal blocksize in Hessian of Lagrangianⓘ	2
Maximal blocksize in Hessian of Lagrangianⓘ	2
Average blocksize in Hessian of Lagrangianⓘ	2.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	8.0000e-03
Maximal coefficientⓘ	1.1000e+01
Infeasibility of initial pointⓘ	19.2
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          3        2        0        1        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          3        2        0        1        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*          7        1        6        0
*
*  Solve m using MINLP minimizing objvar;


Variables  i1,x2,objvar;

Integer Variables  i1;

Equations  e1,e2,e3;


e1.. (-11 + sqr(x2) - 6*x2 + 0.8*i1)*(sqr(3.25*x2 - 0.62*i1) + sqr((-6.35) + 
     0.2*i1 + x2))*(sqr(3.55*x2 - 0.66*i1) + sqr((-6.85) + 0.2*i1 + x2))*(sqr(
     3.6*x2 - 0.7*i1) + sqr((-7.1) + 0.2*i1 + x2))*(sqr(3.8*x2 - 0.82*i1) + 
     sqr((-7.9) + 0.2*i1 + x2)) =E= 0;

e2.. 0.6*i1 - 0.2*x2*i1 + exp((-3) + x2) =L= 1;

e3.. -(2*sqr(x2) + 0.008*POWER(i1,3) - 3.2*x2*i1 - 2*i1) + objvar =E= 0;

* set non-default bounds
i1.lo = 15; i1.up = 25;
x2.lo = 3; x2.up = 5.5;

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;