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Instance: cvxnonsep_pcon40r

separable reformulation of convex MINLP test problem with non-separable power constraint (cvxnonsep_pcon40)
see also problem description (PDF).
Formats ams gms mod nl osil
Primal Bounds
-46.59916883 p1 ( gdx sol )
(infeas: 6e-14)
Dual Bounds
-46.59922362 (ALPHAECP)
-46.60382874 (ANTIGONE)
-46.60382921 (BARON)
-46.59916883 (BONMIN)
-46.59960401 (COUENNE)
-46.59916883 (LINDO)
-46.60329739 (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 79
#Binary Variables 0
#Integer Variables 20
#Nonlinear Variables 40
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 20
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 40
#Nonlinear Nonzeros in Objective 0
#Constraints 40
#Linear Constraints 1
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 39
Operands in Gen. Nonlin. Functions cvpower
Constraints curvature convex
#Nonzeros in Jacobian 156
#Nonlinear Nonzeros in Jacobian 78
#Nonzeros in (Upper-Left) Hessian of Lagrangian 118
#Nonzeros in Diagonal of Hessian of Lagrangian 40
#Blocks in Hessian of Lagrangian 1
Minimal blocksize in Hessian of Lagrangian 40
Maximal blocksize in Hessian of Lagrangian 40
Average blocksize in Hessian of Lagrangian 40.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Infeasibility of initial point 1
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
*         41        1        0       40        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         80       60        0       20        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        197      119       78        0
*
*  Solve m using MINLP minimizing objvar;


Variables  i1,i2,i3,i4,i5,i6,i7,i8,i9,i10,i11,i12,i13,i14,i15,i16,i17,i18,i19
          ,i20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36
          ,x37,x38,x39,x40,objvar,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52
          ,x53,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65,x66,x67,x68,x69
          ,x70,x71,x72,x73,x74,x75,x76,x77,x78,x79,x80;

Positive Variables  x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34
          ,x35,x36,x37,x38,x39,x40;

Integer Variables  i1,i2,i3,i4,i5,i6,i7,i8,i9,i10,i11,i12,i13,i14,i15,i16,i17
          ,i18,i19,i20;

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,e25,e26,e27,e28,e29,e30,e31,e32,e33,e34,e35,e36
          ,e37,e38,e39,e40,e41;


e1..    0.18*i1 + 0.72*i2 + 0.47*i3 + 0.15*i4 + 0.34*i5 + 0.61*i6 + 0.19*i7
      + 0.74*i8 + 0.24*i9 + 0.92*i10 + 0.27*i11 + 0.77*i12 + 0.19*i13
      + 0.29*i14 + 0.09*i15 + 0.58*i16 + 0.68*i17 + 0.55*i18 + 0.43*i19
      + 0.64*i20 + 0.65*x21 + 0.68*x22 + 0.64*x23 + 0.95*x24 + 0.21*x25
      + 0.71*x26 + 0.24*x27 + 0.12*x28 + 0.61*x29 + 0.45*x30 + 0.46*x31
      + 0.66*x32 + 0.77*x33 + 0.35*x34 + 0.66*x35 + 0.42*x36 + 0.84*x37
      + 0.83*x38 + 0.26*x39 + 0.61*x40 + objvar =E= 0;

e2..    x42 + x43 + x44 + x45 + x46 + x47 + x48 + x49 + x50 + x51 + x52 + x53
      + x54 + x55 + x56 + x57 + x58 + x59 + x60 + x61 + x62 + x63 + x64 + x65
      + x66 + x67 + x68 + x69 + x70 + x71 + x72 + x73 + x74 + x75 + x76 + x77
      + x78 + x79 + x80 =L= 480;

e3.. 2**(i1 + i2) - x42 =L= 0;

e4.. 2**(i2 + i3) - x43 =L= 0;

e5.. 2**(i3 + i4) - x44 =L= 0;

e6.. 2**(i4 + i5) - x45 =L= 0;

e7.. 2**(i5 + i6) - x46 =L= 0;

e8.. 2**(i6 + i7) - x47 =L= 0;

e9.. 2**(i7 + i8) - x48 =L= 0;

e10.. 2**(i8 + i9) - x49 =L= 0;

e11.. 2**(i9 + i10) - x50 =L= 0;

e12.. 2**(i10 + i11) - x51 =L= 0;

e13.. 2**(i11 + i12) - x52 =L= 0;

e14.. 2**(i12 + i13) - x53 =L= 0;

e15.. 2**(i13 + i14) - x54 =L= 0;

e16.. 2**(i14 + i15) - x55 =L= 0;

e17.. 2**(i15 + i16) - x56 =L= 0;

e18.. 2**(i16 + i17) - x57 =L= 0;

e19.. 2**(i17 + i18) - x58 =L= 0;

e20.. 2**(i18 + i19) - x59 =L= 0;

e21.. 2**(i19 + i20) - x60 =L= 0;

e22.. 2**(i20 + x21) - x61 =L= 0;

e23.. 2**(x21 + x22) - x62 =L= 0;

e24.. 2**(x22 + x23) - x63 =L= 0;

e25.. 2**(x23 + x24) - x64 =L= 0;

e26.. 2**(x24 + x25) - x65 =L= 0;

e27.. 2**(x25 + x26) - x66 =L= 0;

e28.. 2**(x26 + x27) - x67 =L= 0;

e29.. 2**(x27 + x28) - x68 =L= 0;

e30.. 2**(x28 + x29) - x69 =L= 0;

e31.. 2**(x29 + x30) - x70 =L= 0;

e32.. 2**(x30 + x31) - x71 =L= 0;

e33.. 2**(x31 + x32) - x72 =L= 0;

e34.. 2**(x32 + x33) - x73 =L= 0;

e35.. 2**(x33 + x34) - x74 =L= 0;

e36.. 2**(x34 + x35) - x75 =L= 0;

e37.. 2**(x35 + x36) - x76 =L= 0;

e38.. 2**(x36 + x37) - x77 =L= 0;

e39.. 2**(x37 + x38) - x78 =L= 0;

e40.. 2**(x38 + x39) - x79 =L= 0;

e41.. 2**(x39 + x40) - x80 =L= 0;

* set non-default bounds
i1.up = 5;
i2.up = 5;
i3.up = 5;
i4.up = 5;
i5.up = 5;
i6.up = 5;
i7.up = 5;
i8.up = 5;
i9.up = 5;
i10.up = 5;
i11.up = 5;
i12.up = 5;
i13.up = 5;
i14.up = 5;
i15.up = 5;
i16.up = 5;
i17.up = 5;
i18.up = 5;
i19.up = 5;
i20.up = 5;
x21.up = 5;
x22.up = 5;
x23.up = 5;
x24.up = 5;
x25.up = 5;
x26.up = 5;
x27.up = 5;
x28.up = 5;
x29.up = 5;
x30.up = 5;
x31.up = 5;
x32.up = 5;
x33.up = 5;
x34.up = 5;
x35.up = 5;
x36.up = 5;
x37.up = 5;
x38.up = 5;
x39.up = 5;
x40.up = 5;

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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