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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance st_e42

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	18.78420000 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	18.78419998 (ANTIGONE) 18.78419996 (BARON) 18.78419999 (COUENNE) 18.78420000 (GUROBI) 18.78420000 (LINDO) 18.78420000 (SCIP)
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. Tawarmalani, M and Ahmed, S, Analysis of a machining process, 1997. Project Report on Design of Experiments.
Sourceⓘ	BARON book instance misc/e42
Added to libraryⓘ	03 Sep 2002
Problem typeⓘ	QCP
#Variablesⓘ	7
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	4
#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ⓘ	indefinite
#Nonzeros in Jacobianⓘ	8
#Nonlinear Nonzeros in Jacobianⓘ	4
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	6
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	0
#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ⓘ	1.0000e+00
Maximal coefficientⓘ	5.1571e+01
Infeasibility of initial pointⓘ	72.82
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          3        3        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          8        8        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         11        7        4        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,objvar;

Positive Variables  x1,x2,x3,x4,x7;

Equations  e1,e2,e3;


e1.. 51.5712*x3*x5 + 20.7324*x3 - 25.7856*x5 + 14.9251*x3*x7 - 22.2988*x7 - 
     10.1409*x6*x7 + 42.3401*x6 - x1 + x2 - 6.6425*x4 =E= -72.82;

e2..    x3 =E= 1;

e3..  - x1 - x2 + objvar =E= 0;

* set non-default bounds
x3.up = 1;
x4.up = 1;
x5.lo = -1; x5.up = 1;
x6.lo = -1; x6.up = 1;
x7.up = 3;

Model m / all /;

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

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

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