MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

Home // Instances // Documentation // Download // Statistics

Instance st_e15

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	7.66718007 p1 ( gdx sol ) (infeas: 2e-16)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	7.66718007 (ANTIGONE) 7.66718007 (BARON) 7.66718007 (COUENNE) 7.66718007 (LINDO) 7.66718007 (SCIP) 3.93111209 (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/e15
Added to libraryⓘ	01 Sep 2002
Problem typeⓘ	MBNLP
#Variablesⓘ	5
#Binary Variablesⓘ	3
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	2
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	linear
Objective curvatureⓘ	linear
#Nonzeros in Objectiveⓘ	5
#Nonlinear Nonzeros in Objectiveⓘ	0
#Constraintsⓘ	5
#Linear Constraintsⓘ	3
#Quadratic Constraintsⓘ	1
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	1
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	11
#Nonlinear Nonzeros in Jacobianⓘ	2
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	2
#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ⓘ	1
Average blocksize in Hessian of Lagrangianⓘ	1.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	5.0000e-01
Maximal coefficientⓘ	3.0000e+00
Infeasibility of initial pointⓘ	3
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          6        3        0        3        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          6        3        3        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         17       15        2        0
*
*  Solve m using MINLP minimizing objvar;


Variables  x1,x2,b3,b4,b5,objvar;

Positive Variables  x1,x2;

Binary Variables  b3,b4,b5;

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


e1..  - 2*x1 - 3*x2 - 1.5*b3 - 2*b4 + 0.5*b5 + objvar =E= 0;

e2.. sqr(x1) + b3 =E= 1.25;

e3.. x2**1.5 + 1.5*b4 =E= 3;

e4..    x1 + b3 =L= 1.6;

e5..    1.333*x2 + b4 =L= 3;

e6..  - b3 - b4 + b5 =L= 0;

* set non-default bounds
x1.up = 10;
x2.up = 10;

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;