MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance st_e38

Formatsⓘ	ams gms mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	7197.72714900 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	7197.72714900 (ANTIGONE) 7197.72714900 (BARON) 7197.72714900 (COUENNE) 7197.72714900 (LINDO) 7197.72714900 (SCIP) 3422.67454400 (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. Sandgren, E, Nonlinear Integer and Discrete Programming in Mechanical Design Optimization, Journal of Mechanical Design, 112:2, 1990, 223-229.
Sourceⓘ	BARON book instance misc/e38
Added to libraryⓘ	01 Sep 2002
Problem typeⓘ	MINLP
#Variablesⓘ	4
#Binary Variablesⓘ	0
#Integer Variablesⓘ	2
#Nonlinear Variablesⓘ	4
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	2
Objective Senseⓘ	min
Objective typeⓘ	polynomial
Objective curvatureⓘ	indefinite
#Nonzeros in Objectiveⓘ	4
#Nonlinear Nonzeros in Objectiveⓘ	4
#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ⓘ	6
#Nonlinear Nonzeros in Jacobianⓘ	2
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	10
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	2
#Blocks in Hessian of Lagrangianⓘ	1
Minimal blocksize in Hessian of Lagrangianⓘ	4
Maximal blocksize in Hessian of Lagrangianⓘ	4
Average blocksize in Hessian of Lagrangianⓘ	4.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	9.5400e-03
Maximal coefficientⓘ	3.1416e+00
Infeasibility of initial pointⓘ	9.274e+05
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          4        1        1        2        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          5        3        0        2        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         11        5        6        0
*
*  Solve m using MINLP minimizing objvar;


Variables  i1,i2,x3,x4,objvar;

Integer Variables  i1,i2;

Equations  e1,e2,e3,e4;


e1..  - 0.0625*i1 + 0.0193*x3 =L= 0;

e2..  - 0.0625*i2 + 0.00954*x3 =L= 0;

e3.. 3.1415927*(sqr(x3)*x4 + 1.33333333333333*POWER(x3,3)) =G= 1296000;

e4.. -(0.0389*i1*x3*x4 + 0.1111312*sqr(x3)*i2 + 0.012348046875*sqr(i1)*x4 + 
     0.0775*sqr(i1)*x3) + objvar =E= 0;

* set non-default bounds
i1.lo = 18; i1.up = 100;
i2.lo = 10; i2.up = 100;
x3.lo = 40; x3.up = 80;
x4.lo = 20; x4.up = 60;

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;