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Instance cvxnonsep_psig20r

separable reformulation of convex MINLP test problem with non-separable signomial objective function (cvxnonsep_psig20)
see also problem description (PDF).
Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
95.89738736 p1 ( gdx sol )
(infeas: 1e-17)
Other points (infeas > 1e-08)  
Dual Bounds
95.88916941 (ALPHAECP)
95.89738726 (ANTIGONE)
95.89738726 (BARON)
95.89738736 (BONMIN)
95.89492279 (COUENNE)
95.89738736 (LINDO)
95.89732016 (SCIP)
95.89080128 (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 42
#Binary Variables 0
#Integer Variables 10
#Nonlinear Variables 21
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 10
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 21
#Nonlinear Nonzeros in Objective 0
#Constraints 22
#Linear Constraints 1
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 21
Operands in Gen. Nonlin. Functions log
Constraints curvature convex
#Nonzeros in Jacobian 63
#Nonlinear Nonzeros in Jacobian 21
#Nonzeros in (Upper-Left) Hessian of Lagrangian 21
#Nonzeros in Diagonal of Hessian of Lagrangian 21
#Blocks in Hessian of Lagrangian 21
Minimal blocksize in Hessian of Lagrangian 1
Maximal blocksize in Hessian of Lagrangian 1
Average blocksize in Hessian of Lagrangian 1.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 2.2000e-02
Maximal coefficient 2.0000e+04
Infeasibility of initial point 18.42
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
*         23        1        0       22        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         43       33        0       10        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         85       64       21        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,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36
          ,x37,x38,x39,x40,x41,x42,objvar;

Negative Variables  x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35
          ,x36,x37,x38,x39,x40,x41;

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

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


e1..    i1 + i2 + i3 + i4 + i5 + i6 + i7 + i8 + i9 + i10 + x11 + x12 + x13
      + x14 + x15 + x16 + x17 + x18 + x19 + x20 + 20000*x21 - objvar =E= 0;

e2..    x22 + x23 + x24 + x25 + x26 + x27 + x28 + x29 + x30 + x31 + x32 + x33
      + x34 + x35 + x36 + x37 + x38 + x39 + x40 + x41 + x42 =L= 0;

e3.. -0.32*log(i1) - x22 =L= 0;

e4.. -0.19*log(i2) - x23 =L= 0;

e5.. -0.405*log(i3) - x24 =L= 0;

e6.. -0.265*log(i4) - x25 =L= 0;

e7.. -0.175*log(i5) - x26 =L= 0;

e8.. -0.44*log(i6) - x27 =L= 0;

e9.. -0.275*log(i7) - x28 =L= 0;

e10.. -0.47*log(i8) - x29 =L= 0;

e11.. -0.31*log(i9) - x30 =L= 0;

e12.. -0.295*log(i10) - x31 =L= 0;

e13.. -0.105*log(x11) - x32 =L= 0;

e14.. -0.15*log(x12) - x33 =L= 0;

e15.. -0.235*log(x13) - x34 =L= 0;

e16.. -0.115*log(x14) - x35 =L= 0;

e17.. -0.42*log(x15) - x36 =L= 0;

e18.. -0.095*log(x16) - x37 =L= 0;

e19.. -0.115*log(x17) - x38 =L= 0;

e20.. -0.085*log(x18) - x39 =L= 0;

e21.. -0.115*log(x19) - x40 =L= 0;

e22.. -0.022*log(x20) - x41 =L= 0;

e23.. -log(x21) - x42 =L= 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;
x11.lo = 1; x11.up = 10;
x12.lo = 1; x12.up = 10;
x13.lo = 1; x13.up = 10;
x14.lo = 1; x14.up = 10;
x15.lo = 1; x15.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 = 1E-8;

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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