MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance: cvxnonsep_psig30

convex MINLP test problem with non-separable signomial objective function
see also problem description (PDF).
Formats ams gms mod nl osil
Primal Bounds
80.29684365 p1 ( gdx sol )
(infeas: 0)
78.99917013 p2 ( gdx sol )
(infeas: 0)
78.99885434 p3 ( gdx sol )
(infeas: 0)
Dual Bounds
21.22877966 (ALPHAECP)
78.99127101 (BARON)
78.99885434 (BONMIN)
78.99356140 (LINDO)
67.28962647 (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 30
#Binary Variables 0
#Integer Variables 15
#Nonlinear Variables 30
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 15
Objective Sense min
Objective type signomial
Objective curvature convex
#Nonzeros in Objective 30
#Nonlinear Nonzeros in Objective 30
#Constraints 0
#Linear Constraints 0
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature linear
#Nonzeros in Jacobian 0
#Nonlinear Nonzeros in Jacobian 0
#Nonzeros in (Upper-Left) Hessian of Lagrangian 900
#Nonzeros in Diagonal of Hessian of Lagrangian 30
#Blocks in Hessian of Lagrangian 1
Minimal blocksize in Hessian of Lagrangian 30
Maximal blocksize in Hessian of Lagrangian 30
Average blocksize in Hessian of Lagrangian 30.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Infeasibility of initial point 0
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
*          1        1        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         31       16        0       15        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         31        1       30        0
*
*  Solve m using MINLP minimizing objvar;


Variables  i1,i2,i3,i4,i5,i6,i7,i8,i9,i10,i11,i12,i13,i14,i15,x16,x17,x18,x19
          ,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,objvar;

Integer Variables  i1,i2,i3,i4,i5,i6,i7,i8,i9,i10,i11,i12,i13,i14,i15;

Equations  e1;


e1.. 30000*i1**(-0.48)*i2**(-0.275)*i3**(-0.26)*i4**(-0.215)*i5**(-0.245)*i6**(
     -0.31)*i7**(-0.34)*i8**(-0.2)*i9**(-0.185)*i10**(-0.495)*i11**(-0.02)*i12
     **(-0.445)*i13**(-0.455)*i14**(-0.4)*i15**(-0.05)*x16**(-0.13)*x17**(-0.17
     )*x18**(-0.34)*x19**(-0.07)*x20**(-0.36)*x21**(-0.05)*x22**(-0.325)*x23**(
     -0.245)*x24**(-0.39)*x25**(-0.36)*x26**(-0.45)*x27**(-0.445)*x28**(-0.165)
     *x29**(-0.35)*x30**(-0.1) + i1 + i2 + i3 + i4 + i5 + i6 + i7 + i8 + i9 + 
     i10 + i11 + i12 + i13 + i14 + i15 + x16 + x17 + x18 + x19 + x20 + x21 + 
     x22 + x23 + x24 + x25 + x26 + x27 + x28 + x29 + x30 - objvar =E= 0;

* 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;
i11.lo = 1; i11.up = 10;
i12.lo = 1; i12.up = 10;
i13.lo = 1; i13.up = 10;
i14.lo = 1; i14.up = 10;
i15.lo = 1; i15.up = 10;
x16.lo = 1; x16.up = 10;
x17.lo = 1; x17.up = 10;
x18.lo = 1; x18.up = 10;
x19.lo = 1; x19.up = 10;
x20.lo = 1; x20.up = 10;
x21.lo = 1; x21.up = 10;
x22.lo = 1; x22.up = 10;
x23.lo = 1; x23.up = 10;
x24.lo = 1; x24.up = 10;
x25.lo = 1; x25.up = 10;
x26.lo = 1; x26.up = 10;
x27.lo = 1; x27.up = 10;
x28.lo = 1; x28.up = 10;
x29.lo = 1; x29.up = 10;
x30.lo = 1; x30.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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