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Instance cvxnonsep_nsig30

convex MINLP test problem with non-separable signomial constraint function
see also problem description (PDF).
Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
133.31874180 p1 ( gdx sol )
(infeas: 1e-16)
131.61545530 p2 ( gdx sol )
(infeas: 0)
130.63345720 p3 ( gdx sol )
(infeas: 0)
130.62871260 p4 ( gdx sol )
(infeas: 1e-10)
Other points (infeas > 1e-08)  
Dual Bounds
125.76693430 (ALPHAECP)
16.86054456 (ANTIGONE)
130.62871250 (BARON)
130.62871260 (BONMIN)
130.62871260 (LINDO)
126.08023180 (SCIP)
130.62821640 (SHOT)
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 linear
Objective curvature linear
#Nonzeros in Objective 30
#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 30
#Nonlinear Nonzeros in Jacobian 30
#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
Minimal coefficient 4.0000e-03
Maximal coefficient 1.8800e+00
Infeasibility of initial point 0.9989
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
*         31       16        0       15        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         61       31       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,e2;


e1..    1.29*i1 + 0.76*i2 + i3 + 1.62*i4 + 1.07*i5 + 0.7*i6 + 1.88*i7 + 1.75*i8
      + 1.1*i9 + 1.24*i10 + 1.17*i11 + 0.82*i12 + 1.06*i13 + 0.94*i14
      + 0.46*i15 + 1.69*x16 + 0.39*x17 + 0.45*x18 + 0.34*x19 + 0.46*x20
      + 1.86*x21 + 1.46*x22 + 0.98*x23 + 1.16*x24 + 0.47*x25 + 0.92*x26
      + 1.43*x27 + 1.81*x28 + 1.78*x29 + 0.67*x30 - objvar =E= 0;

e2.. -0.2*i1**0.028*i2**0.041*i3**0.047*i4**0.022*i5**0.041*i6**0.026*i7**0.052
     *i8**0.051*i9**0.016*i10**0.038*i11**0.036*i12**0.033*i13**0.054*i14**
     0.016*i15**0.02*x16**0.007*x17**0.058*x18**0.04*x19**0.03*x20**0.039*x21**
     0.034*x22**0.04*x23**0.034*x24**0.044*x25**0.032*x26**0.061*x27**0.013*x28
     **0.007*x29**0.007*x30**0.004 =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;
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 = 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;
x21.lo = 1E-5; x21.up = 10;
x22.lo = 1E-5; x22.up = 10;
x23.lo = 1E-5; x23.up = 10;
x24.lo = 1E-5; x24.up = 10;
x25.lo = 1E-5; x25.up = 10;
x26.lo = 1E-5; x26.up = 10;
x27.lo = 1E-5; x27.up = 10;
x28.lo = 1E-5; x28.up = 10;
x29.lo = 1E-5; x29.up = 10;
x30.lo = 1E-5; 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;


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