MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance: cvxnonsep_nsig20

convex MINLP test problem with non-separable signomial constraint function
see also problem description (PDF).
Formats ams gms mod nl osil
Primal Bounds
80.94929546 p1 ( gdx sol )
(infeas: 0)
Dual Bounds
80.93271244 (ALPHAECP)
80.83748925 (ANTIGONE)
80.94120134 (BARON)
80.94929545 (BONMIN)
80.94431304 (LINDO)
80.94657535 (SCIP)
References Kronqvist, Jan, Lundell, Andreas, and Westerlund, Tapio, Reformulations for utilizing separability when solving convex MINLP problems, submitted, 2017.
Application Test Problem
Added to library 11 Sep 2017
Problem type MINLP
#Variables 20
#Binary Variables 0
#Integer Variables 10
#Nonlinear Variables 20
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 10
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 20
#Nonlinear Nonzeros in Objective 0
#Constraints 1
#Linear Constraints 0
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 1
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature convex
#Nonzeros in Jacobian 20
#Nonlinear Nonzeros in Jacobian 20
#Nonzeros in (Upper-Left) Hessian of Lagrangian 400
#Nonzeros in Diagonal of Hessian of Lagrangian 20
#Blocks in Hessian of Lagrangian 1
Minimal blocksize in Hessian of Lagrangian 20
Maximal blocksize in Hessian of Lagrangian 20
Average blocksize in Hessian of Lagrangian 20.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Infeasibility of initial point 0.9985
Sparsity Jacobian Sparsity of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of Hessian of Lagrangian

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          2        1        0        1        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         21       11        0       10        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         41       21       20        0
*
*  Solve m using MINLP minimizing objvar;


Variables  i1,i2,i3,i4,i5,i6,i7,i8,i9,i10,x11,x12,x13,x14,x15,x16,x17,x18,x19
          ,x20,objvar;

Integer Variables  i1,i2,i3,i4,i5,i6,i7,i8,i9,i10;

Equations  e1,e2;


e1..    1.5*i1 + 0.51*i2 + 1.01*i3 + 1.4*i4 + 1.78*i5 + 1.92*i6 + 1.09*i7
      + 0.48*i8 + 0.67*i9 + 0.52*i10 + 1.68*x11 + 0.51*x12 + 1.63*x13
      + 0.49*x14 + 1.86*x15 + 0.7*x16 + 0.39*x17 + 0.5*x18 + 1.23*x19
      + 0.95*x20 - objvar =E= 0;

e2.. -0.2*i1**0.065*i2**0.004*i3**0.084*i4**0.093*i5**0.06*i6**0.075*i7**0.074*
     i8**0.039*i9**0.065*i10**0.017*x11**0.07*x12**0.03*x13**0.028*x14**0.005*
     x15**0.01*x16**0.082*x17**0.069*x18**0.032*x19**0.095*x20**0.003 =L= -1;

* set non-default bounds
i1.lo = 1; i1.up = 10;
i2.lo = 1; i2.up = 10;
i3.lo = 1; i3.up = 10;
i4.lo = 1; i4.up = 10;
i5.lo = 1; i5.up = 10;
i6.lo = 1; i6.up = 10;
i7.lo = 1; i7.up = 10;
i8.lo = 1; i8.up = 10;
i9.lo = 1; i9.up = 10;
i10.lo = 1; i10.up = 10;
x11.lo = 1E-5; x11.up = 10;
x12.lo = 1E-5; x12.up = 10;
x13.lo = 1E-5; x13.up = 10;
x14.lo = 1E-5; x14.up = 10;
x15.lo = 1E-5; x15.up = 10;
x16.lo = 1E-5; x16.up = 10;
x17.lo = 1E-5; x17.up = 10;
x18.lo = 1E-5; x18.up = 10;
x19.lo = 1E-5; x19.up = 10;
x20.lo = 1E-5; x20.up = 10;

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;


Last updated: 2018-09-14 Git hash: ac5a5314
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