MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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

Instance st_e27

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	2. p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	2. (ANTIGONE) 2. (BARON) 2. (COUENNE) 2. (CPLEX) 2. (GUROBI) 2. (LINDO) 2. (SCIP) 2. (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. Falk, J E and Soland, R M, An algorithm for separable nonconvex programming problems, Management Science, 15:9, 1969, 550-569.
Sourceⓘ	BARON book instance misc/e27
Added to libraryⓘ	01 Sep 2002
Problem typeⓘ	MBQP
#Variablesⓘ	4
#Binary Variablesⓘ	2
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	2
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	quadratic
Objective curvatureⓘ	concave
#Nonzeros in Objectiveⓘ	4
#Nonlinear Nonzeros in Objectiveⓘ	2
#Constraintsⓘ	6
#Linear Constraintsⓘ	6
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	linear
#Nonzeros in Jacobianⓘ	12
#Nonlinear Nonzeros in Jacobianⓘ	0
#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ⓘ	1.0000e+00
Maximal coefficientⓘ	6.0000e+00
Infeasibility of initial pointⓘ	0
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          7        1        0        6        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          5        3        2        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         17       15        2        0
*
*  Solve m using MINLP minimizing objvar;


Variables  b1,b2,x3,x4,objvar;

Positive Variables  x3,x4;

Binary Variables  b1,b2;

Equations  e1,e2,e3,e4,e5,e6,e7;


e1..  - x3 + 3*x4 =L= 5;

e2..    2*x3 - x4 =L= 5;

e3..  - 2*x3 + x4 =L= 0;

e4..    x3 - 3*x4 =L= 0;

e5..  - 6*b1 + x3 =L= 0;

e6..  - 5*b2 + x4 =L= 0;

e7.. -(4*x3 - sqr(x3) - sqr(x4) + 2*x4) - 2*b1 - 2*b2 + objvar =E= 2;

* set non-default bounds
x3.up = 6;
x4.up = 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;