MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance st_e29

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-0.94347050 p1 ( gdx sol ) (infeas: 6e-15)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-0.94347050 (ANTIGONE) -0.94347050 (BARON) -0.94347050 (COUENNE) -0.94347050 (LINDO) -0.94347050 (SCIP) -0.99430989 (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. Ashrafi, Noushin and Berman, Oded, Optimization models for selection of programs, considering cost and reliability, IEEE Transactions on Reliability, 41:2, 1992, 281-287.
Sourceⓘ	BARON book instance misc/e29
Added to libraryⓘ	01 Sep 2002
Problem typeⓘ	MBNLP
#Variablesⓘ	11
#Binary Variablesⓘ	8
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	3
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	polynomial
Objective curvatureⓘ	indefinite
#Nonzeros in Objectiveⓘ	3
#Nonlinear Nonzeros in Objectiveⓘ	3
#Constraintsⓘ	7
#Linear Constraintsⓘ	4
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	3
Operands in Gen. Nonlin. Functionsⓘ	log
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	27
#Nonlinear Nonzeros in Jacobianⓘ	3
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	9
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	3
#Blocks in Hessian of Lagrangianⓘ	1
Minimal blocksize in Hessian of Lagrangianⓘ	3
Maximal blocksize in Hessian of Lagrangianⓘ	3
Average blocksize in Hessian of Lagrangianⓘ	3.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	1.0000e+00
Maximal coefficientⓘ	3.9120e+00
Infeasibility of initial pointⓘ	1
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          8        3        0        5        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         12        4        8        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         31       25        6        0
*
*  Solve m using MINLP minimizing objvar;


Variables  x1,x2,x3,b4,b5,b6,b7,b8,b9,b10,b11,objvar;

Positive Variables  x1,x2,x3;

Binary Variables  b4,b5,b6,b7,b8,b9,b10,b11;

Equations  e1,e2,e3,e4,e5,e6,e7,e8;


e1.. x1*x2*x3 + objvar =E= 0;

e2.. -log(1 - x1) - 2.30258509299405*b4 - 1.6094379124341*b5
      - 1.89711998488588*b6 =E= 0;

e3.. -log(1 - x2) - 2.99573227355399*b7 - 1.6094379124341*b8
      - 1.89711998488588*b9 =E= 0;

e4.. -log(1 - x3) - 3.91202300542815*b10 - 2.81341071676004*b11 =L= 0;

e5..  - b4 - b5 - b6 =L= -1;

e6..  - b7 - b8 - b9 =L= -1;

e7..  - b10 - b11 =L= -1;

e8..    3*b4 + b5 + 2*b6 + 3*b7 + 2*b8 + b9 + 3*b10 + 2*b11 =L= 10;

* set non-default bounds
x1.up = 0.997;
x2.up = 0.9985;
x3.up = 0.9988;

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;