MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance synthes2

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	73.03531253 p1 ( gdx sol ) (infeas: 1e-13)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	73.03504110 (ALPHAECP) 73.03531245 (ANTIGONE) 73.03531245 (BARON) 73.03531252 (BONMIN) 73.03531253 (COUENNE) 73.03531253 (LINDO) 73.03530997 (SCIP) 73.03529225 (SHOT)
Referencesⓘ	Duran, Marco A and Grossmann, I E, An Outer-Approximation Algorithm for a Class of Mixed-integer Nonlinear Programs, Mathematical Programming, 36:3, 1986, 307-339.
Sourceⓘ	MacMINLP model synthes2.mod
Applicationⓘ	Synthesis of processing system
Added to libraryⓘ	01 May 2001
Problem typeⓘ	MBNLP
#Variablesⓘ	11
#Binary Variablesⓘ	5
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	4
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	nonlinear
Objective curvatureⓘ	convex
#Nonzeros in Objectiveⓘ	11
#Nonlinear Nonzeros in Objectiveⓘ	4
#Constraintsⓘ	14
#Linear Constraintsⓘ	11
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	3
Operands in Gen. Nonlin. Functionsⓘ	exp log
Constraints curvatureⓘ	convex
#Nonzeros in Jacobianⓘ	37
#Nonlinear Nonzeros in Jacobianⓘ	4
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	6
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	4
#Blocks in Hessian of Lagrangianⓘ	3
Minimal blocksize in Hessian of Lagrangianⓘ	1
Maximal blocksize in Hessian of Lagrangianⓘ	2
Average blocksize in Hessian of Lagrangianⓘ	1.333333
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	2.0000e-01
Maximal coefficientⓘ	6.0000e+01
Infeasibility of initial pointⓘ	1
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         15        2        0       13        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         12        7        5        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         49       41        8        0
*
*  Solve m using MINLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,b7,b8,b9,b10,b11,objvar;

Positive Variables  x1,x2,x3,x4,x5,x6;

Binary Variables  b7,b8,b9,b10,b11;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15;


e1.. -log(1 + x4 + x5) =L= 0;

e2.. exp(x1) - 10*b7 =L= 1;

e3.. exp(0.833333*x2) - 10*b8 =L= 1;

e4..    1.25*x3 - 10*b9 =L= 0;

e5..    x4 + x5 - 10*b10 =L= 0;

e6..  - 2*x3 + 2*x6 - 10*b11 =L= 0;

e7..  - x1 - x2 - 2*x3 + x4 + 2*x6 =L= 0;

e8..  - x1 - x2 - 0.75*x3 + x4 + 2*x6 =L= 0;

e9..    x3 - x6 =L= 0;

e10..    2*x3 - x4 - 2*x6 =L= 0;

e11..  - 0.5*x4 + x5 =L= 0;

e12..  - 0.2*x4 - x5 =L= 0;

e13..    b7 + b8 =E= 1;

e14..    b10 + b11 =L= 1;

e15.. -(exp(x1) - 10*x1 + exp(0.833333*x2) - 15*x2 - 60*log(1 + x4 + x5) + 15*
      x4 + 5*x5) + 15*x3 + 20*x6 - 5*b7 - 8*b8 - 6*b9 - 10*b10 - 6*b11 + objvar
       =E= 140;

* set non-default bounds
x1.up = 2;
x2.up = 2;
x3.up = 2;
x6.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 MINLP $set MINLP MINLP
Solve m using %MINLP% minimizing objvar;