MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance synthes3

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	68.00974052 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	68.00946700 (ALPHAECP) 68.00974045 (ANTIGONE) 68.00974045 (BARON) 68.00974052 (BONMIN) 68.00974052 (COUENNE) 68.00974052 (LINDO) 68.00974052 (SCIP) 68.00941454 (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 synthes3.mod
Applicationⓘ	Synthesis of processing system
Added to libraryⓘ	01 May 2001
Problem typeⓘ	MBNLP
#Variablesⓘ	17
#Binary Variablesⓘ	8
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	6
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	nonlinear
Objective curvatureⓘ	convex
#Nonzeros in Objectiveⓘ	17
#Nonlinear Nonzeros in Objectiveⓘ	6
#Constraintsⓘ	23
#Linear Constraintsⓘ	19
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	4
Operands in Gen. Nonlin. Functionsⓘ	exp log
Constraints curvatureⓘ	convex
#Nonzeros in Jacobianⓘ	73
#Nonlinear Nonzeros in Jacobianⓘ	6
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	8
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	6
#Blocks in Hessian of Lagrangianⓘ	5
Minimal blocksize in Hessian of Lagrangianⓘ	1
Maximal blocksize in Hessian of Lagrangianⓘ	2
Average blocksize in Hessian of Lagrangianⓘ	1.2
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	1.6000e-01
Maximal coefficientⓘ	9.0000e+01
Infeasibility of initial pointⓘ	1
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         24        3        0       21        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         18       10        8        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         91       79       12        0
*
*  Solve m using MINLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,b10,b11,b12,b13,b14,b15,b16,b17,objvar;

Positive Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9;

Binary Variables  b10,b11,b12,b13,b14,b15,b16,b17;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19
          ,e20,e21,e22,e23,e24;


e1.. (-1.5*log(1 + x5)) - log(1 + x6) - x8 =L= 0;

e2.. -log(1 + x3 + x4) =L= 0;

e3..  - x1 - x2 + x3 + 2*x4 + 0.8*x5 + 0.8*x6 - 0.5*x7 - x8 - 2*x9 =L= 0;

e4..  - x1 - x2 + 2*x4 + 0.8*x5 + 0.8*x6 - 2*x7 - x8 - 2*x9 =L= 0;

e5..  - 2*x4 - 0.8*x5 - 0.8*x6 + 2*x7 + x8 + 2*x9 =L= 0;

e6..  - 0.8*x5 - 0.8*x6 + x8 =L= 0;

e7..  - x4 + x7 + x9 =L= 0;

e8..  - 0.4*x5 - 0.4*x6 + 1.5*x8 =L= 0;

e9..    0.16*x5 + 0.16*x6 - 1.2*x8 =L= 0;

e10..    x3 - 0.8*x4 =L= 0;

e11..  - x3 + 0.4*x4 =L= 0;

e12.. exp(x1) - 10*b10 =L= 1;

e13.. exp(0.833333*x2) - 10*b11 =L= 1;

e14..    x7 - 10*b12 =L= 0;

e15..    0.8*x5 + 0.8*x6 - 10*b13 =L= 0;

e16..    2*x4 - 2*x7 - 2*x9 - 10*b14 =L= 0;

e17..    x5 - 10*b15 =L= 0;

e18..    x6 - 10*b16 =L= 0;

e19..    x3 + x4 - 10*b17 =L= 0;

e20..    b10 + b11 =E= 1;

e21..    b13 + b14 =L= 1;

e22..  - b13 + b15 + b16 =E= 0;

e23..    b12 - b17 =L= 0;

e24.. -(exp(x1) - 10*x1 + exp(0.833333*x2) - 15*x2 - 65*log(1 + x3 + x4) + 15*
      x3 + 80*x4 - 90*log(1 + x5) + 25*x5 - 80*log(1 + x6) + 35*x6) + 40*x7
       - 15*x8 + 35*x9 - 5*b10 - 8*b11 - 6*b12 - 10*b13 - 6*b14 - 7*b15 - 4*b16
       - 5*b17 + objvar =E= 120;

* set non-default bounds
x1.up = 2;
x2.up = 2;
x3.up = 1;
x4.up = 2;
x5.up = 2;
x6.up = 2;
x7.up = 2;
x8.up = 1;
x9.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;