st_testgr3.gms:
References:
- Tawarmalani, M, and Sahinidis, N, Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications. Kluwer, 2002.
- Shectman, J P, Finite Algorithms for Global Optimization of Concave Programs and General Quadratic Programs, 1999. PhD thesis, Department of Mechanical and Industrial Engineering, University of Illinois, Urbana Champagne
Point:
p1
Best known point (p1): Solution value -20.59 (global optimum, BARON certificate)
<![CDATA[
$offlisting
* MINLP written by GAMS Convert at 09/01/02 11:06:08
*
* Equation counts
* Total E G L N X C
* 21 1 0 20 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 21 1 0 20 0 0 0 0
* FX 0 0 0 0 0 0 0 0
*
* Nonzero counts
* Total const NL DLL
* 182 162 20 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,objvar;
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;
e1.. 8*i1 + 5*i6 + 4*i7 + 6*i12 + 6*i13 + 9*i14 + 5*i19 + i20 =L= 220;
e2.. 3*i1 + 4*i2 + 3*i7 + 7*i8 + 4*i13 + 9*i14 + 3*i15 + 2*i20 =L= 175;
e3.. 2*i2 + i3 + 6*i8 + 8*i9 + 9*i14 + 9*i15 + 8*i16 =L= 215;
e4.. 7*i3 + i4 + 7*i9 + 9*i10 + 2*i15 + 4*i16 + 9*i17 =L= 195;
e5.. 4*i4 + 4*i5 + i10 + 3*i11 + 7*i16 + 2*i17 + 8*i18 =L= 145;
e6.. 9*i5 + 5*i6 + 5*i11 + 7*i12 + i17 + 4*i18 + 6*i19 =L= 185;
e7.. 5*i1 + 5*i6 + 3*i7 + 8*i12 + 5*i13 + 9*i18 + 9*i19 + i20 =L= 225;
e8.. i1 + 9*i2 + 9*i7 + 3*i8 + 9*i13 + 7*i14 + 4*i19 + i20 =L= 215;
e9.. 3*i1 + 6*i2 + 3*i3 + 4*i8 + 2*i9 + 6*i14 + 3*i15 + 8*i19 + i20 =L= 175;
e10.. i2 + 2*i3 + 8*i4 + 4*i9 + i10 + 9*i15 + 6*i16 =L= 155;
e11.. 9*i3 + 3*i4 + 6*i5 + i10 + 6*i11 + 9*i16 + 8*i17 =L= 210;
e12.. 6*i4 + 3*i5 + 3*i6 + 6*i11 + 3*i12 + 8*i17 + 9*i18 =L= 190;
e13.. 9*i5 + 8*i6 + 2*i7 + 7*i12 + 8*i13 + 4*i18 + 3*i19 =L= 205;
e14.. 4*i1 + 6*i6 + 9*i7 + i8 + 6*i13 + 9*i14 + 8*i19 + 6*i20 =L= 245;
e15.. 7*i1 + 3*i2 + 7*i7 + 4*i8 + 2*i9 + i14 + 3*i15 + 5*i20 =L= 160;
e16.. 7*i2 + 9*i3 + 7*i8 + 9*i9 + 5*i10 + 2*i15 + 6*i16 =L= 225;
e17.. 6*i3 + 9*i4 + 8*i9 + 4*i10 + 2*i11 + 6*i16 + 4*i17 =L= 195;
e18.. 5*i4 + 5*i5 + 7*i10 + 8*i11 + 9*i12 + 8*i17 + 6*i18 =L= 240;
e19.. 7*i5 + 5*i6 + 6*i11 + 2*i12 + 8*i13 + 6*i18 + 9*i19 =L= 215;
e20.. i1 + i2 + i3 + i4 + i5 + i6 + i7 + i8 + i9 + i10 + i11 + i12 + i13
+ i14 + i15 + i16 + i17 + i18 + i19 + i20 =L= 200;
e21.. - (0.00055*i1*i1 - 0.0583*i1 + 0.0019*i2*i2 - 0.2318*i2 + 0.0002*i3*i3
+ 0.0108*i3 + 0.00095*i4*i4 - 0.1634*i4 + 0.0046*i5*i5 - 0.138*i5 +
0.0035*i6*i6 + 0.357*i6 + 0.00315*i7*i7 - 0.1953*i7 + 0.00475*i8*i8 +
0.361*i8 + 0.0048*i9*i9 - 0.1824*i9 + 0.003*i10*i10 + 0.162*i10 + 0.00265
*i11*i11 - 0.4346*i11 + 0.0017*i12*i12 - 0.1054*i12 + 0.0012*i13*i13 +
0.2376*i13 + 0.00295*i14*i14 - 0.0059*i14 + 0.00315*i15*i15 + 0.189*i15
+ 0.0021*i16*i16 - 0.0252*i16 + 0.00225*i17*i17 - 0.099*i17 + 0.0034*i18
*i18 - 0.3604*i18 + 0.001*i19*i19 + 0.022*i19 + 0.00305*i20*i20 - 0.3294*
i20) + objvar =E= 0;
* set non default bounds
i1.up = 100;
i2.up = 100;
i3.up = 100;
i4.up = 100;
i5.up = 100;
i6.up = 100;
i7.up = 100;
i8.up = 100;
i9.up = 100;
i10.up = 100;
i11.up = 100;
i12.up = 100;
i13.up = 100;
i14.up = 100;
i15.up = 100;
i16.up = 100;
i17.up = 100;
i18.up = 100;
i19.up = 100;
i20.up = 100;
$if set nostart $goto modeldef
* set non default levels
* set non default marginals
$label modeldef
Model m / all /;
m.limrow=0; m.limcol=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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