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Instance: cvxnonsep_normcon40r

separable reformulation of convex MINLP test problem with non-separable 2-norm constraint (cvxnonsep_normcon40)
see also problem description (PDF).
Formats ams gms lp mod nl osil pip
Primal Bounds
-32.62966972 p1 ( gdx sol )
(infeas: 1e-14)
Dual Bounds
-32.63100926 (ALPHAECP)
-32.63293268 (ANTIGONE)
-32.63293301 (BARON)
-32.62966972 (BONMIN)
-32.62983932 (COUENNE)
-32.62966972 (LINDO)
-32.63078754 (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 MIQCP
#Variables 80
#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 41
#Linear Constraints 1
#Quadratic Constraints 40
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature convex
#Nonzeros in Jacobian 120
#Nonlinear Nonzeros in Jacobian 40
#Nonzeros in (Upper-Left) Hessian of Lagrangian 40
#Nonzeros in Diagonal of Hessian of Lagrangian 40
#Blocks in Hessian of Lagrangian 40
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
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
*         42        1        0       41        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         81       61        0       20        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        161      121       40        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,x81;

Positive Variables  x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34
          ,x35,x36,x37,x38,x39,x40,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,x81;

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,e42;


e1..    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 + x81 =L= 99.9999;

e2..  - 0.64*i1 - 0.38*i2 - 0.19*i3 - 0.43*i4 - 0.48*i5 - 0.12*i6 - 0.59*i7
      - 0.23*i8 - 0.38*i9 - 0.85*i10 - 0.25*i11 - 0.29*i12 - 0.62*i13
      - 0.82*i14 - 0.27*i15 - 0.98*i16 - 0.73*i17 - 0.34*i18 - 0.58*i19
      - 0.11*i20 - 0.91*x21 - 0.88*x22 - 0.82*x23 - 0.26*x24 - 0.02*x25
      - 0.43*x26 - 0.31*x27 - 0.59*x28 - 0.16*x29 - 0.18*x30 - 0.42*x31
      - 0.09*x32 - 0.6*x33 - 0.47*x34 - 0.7*x35 - 0.7*x36 - 0.64*x37 - 0.03*x38
      - 0.07*x39 - 0.32*x40 - objvar =E= 0;

e3.. sqr(i1) - x42 =L= 0;

e4.. sqr(i2) - x43 =L= 0;

e5.. sqr(i3) - x44 =L= 0;

e6.. sqr(i4) - x45 =L= 0;

e7.. sqr(i5) - x46 =L= 0;

e8.. sqr(i6) - x47 =L= 0;

e9.. sqr(i7) - x48 =L= 0;

e10.. sqr(i8) - x49 =L= 0;

e11.. sqr(i9) - x50 =L= 0;

e12.. sqr(i10) - x51 =L= 0;

e13.. sqr(i11) - x52 =L= 0;

e14.. sqr(i12) - x53 =L= 0;

e15.. sqr(i13) - x54 =L= 0;

e16.. sqr(i14) - x55 =L= 0;

e17.. sqr(i15) - x56 =L= 0;

e18.. sqr(i16) - x57 =L= 0;

e19.. sqr(i17) - x58 =L= 0;

e20.. sqr(i18) - x59 =L= 0;

e21.. sqr(i19) - x60 =L= 0;

e22.. sqr(i20) - x61 =L= 0;

e23.. sqr(x21) - x62 =L= 0;

e24.. sqr(x22) - x63 =L= 0;

e25.. sqr(x23) - x64 =L= 0;

e26.. sqr(x24) - x65 =L= 0;

e27.. sqr(x25) - x66 =L= 0;

e28.. sqr(x26) - x67 =L= 0;

e29.. sqr(x27) - x68 =L= 0;

e30.. sqr(x28) - x69 =L= 0;

e31.. sqr(x29) - x70 =L= 0;

e32.. sqr(x30) - x71 =L= 0;

e33.. sqr(x31) - x72 =L= 0;

e34.. sqr(x32) - x73 =L= 0;

e35.. sqr(x33) - x74 =L= 0;

e36.. sqr(x34) - x75 =L= 0;

e37.. sqr(x35) - x76 =L= 0;

e38.. sqr(x36) - x77 =L= 0;

e39.. sqr(x37) - x78 =L= 0;

e40.. sqr(x38) - x79 =L= 0;

e41.. sqr(x39) - x80 =L= 0;

e42.. sqr(x40) - x81 =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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