nvs19.gms:
References:
- Tawarmalani, M, and Sahinidis, N, Exact Algorithms for Global Optimization of Mixed-Integer Nonlinear Programs. In Pardalos, P M, and Romeijn, E, Eds, Handbook of Global Optimization - Volume 2: Heuristic Approaches. Kluwer Academic Publishers, 2001.
- Gupta, O K, and Ravindran, A, Branch and Bound Experiments in Convex Nonlinear Integer Programming. Management Science 13 (1985), 1533-1546.
Point:
p1
Best known point (p1): Solution value -1098.40 (global optimum, BARON certificate)
<![CDATA[
$offlisting
* MINLP written by GAMS Convert at 07/24/02 13:01:18
*
* Equation counts
* Total E G L N X C
* 9 1 8 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 9 1 0 8 0 0 0 0
* FX 0 0 0 0 0 0 0 0
*
* Nonzero counts
* Total const NL DLL
* 73 1 72 0
*
* Solve m using MINLP minimizing objvar;
Variables i1,i2,i3,i4,i5,i6,i7,i8,objvar;
Integer Variables i1,i2,i3,i4,i5,i6,i7,i8;
Equations e1,e2,e3,e4,e5,e6,e7,e8,e9;
e1.. (-9*sqr(i1)) - 10*i1*i2 - 8*sqr(i2) - 5*sqr(i3) - 6*i3*i1 - 10*i3*i2 - 7*
sqr(i4) - 10*i4*i1 - 6*i4*i2 - 2*i4*i3 - 2*i5*i2 - 7*sqr(i5) - 6*i6*i1 - 2
*i6*i2 - 2*i6*i4 - 5*sqr(i6) + 6*i7*i1 + 2*i7*i2 + 4*i7*i3 + 2*i7*i4 - 4*
i7*i5 + 4*i7*i6 - 8*sqr(i7) - 2*i8*i1 - 8*i8*i2 - 2*i8*i3 + 6*i8*i5 - 2*i8
*i7 - 6*sqr(i8) =G= -1980;
e2.. (-6*sqr(i1)) - 8*i1*i2 - 6*sqr(i2) - 4*sqr(i3) - 2*i3*i1 - 2*i3*i2 - 8*
sqr(i4) + 2*i4*i1 + 10*i4*i2 - 2*i5*i1 - 6*i5*i2 + 6*i5*i4 + 7*sqr(i5) - 2
*i6*i2 + 8*i6*i3 + 2*i6*i4 - 4*i6*i5 - 8*sqr(i6) - 6*i7*i1 - 10*i7*i2 - 2*
i7*i3 + 10*i7*i4 - 10*i7*i5 - 8*sqr(i7) - 2*i8*i1 - 4*i8*i2 - 2*i8*i3 - 8*
i8*i5 - 8*i8*i7 - 5*sqr(i8) =G= -3180;
e3.. (-9*sqr(i1)) - 6*sqr(i2) - 8*sqr(i3) + 2*i2*i1 + 2*i3*i2 - 6*sqr(i4) + 4*
i4*i1 + 4*i4*i2 - 2*i4*i3 - 6*i5*i1 - 2*i5*i2 + 4*i5*i4 + 6*sqr(i5) + 2*i6
*i1 + 4*i6*i2 - 6*i6*i4 - 2*i6*i5 - 5*sqr(i6) + 2*i7*i2 - 4*i7*i3 - 6*i7*
i5 - 4*i7*i6 - 7*sqr(i7) - 2*i8*i1 + 4*i8*i3 + 2*i8*i4 - 4*sqr(i8)
=G= -1830;
e4.. (-8*sqr(i1)) - 4*sqr(i2) - 9*sqr(i3) - 7*sqr(i4) - 2*i2*i1 - 2*i3*i1 - 4*
i3*i2 + 6*i4*i1 + 2*i4*i2 - 2*i4*i3 - 6*i5*i1 - 4*i5*i2 - 2*i5*i3 + 6*i5*
i4 + 6*sqr(i5) - 10*i6*i1 - 10*i6*i3 + 4*i6*i4 - 2*i6*i5 - 7*sqr(i6) + 6*
i7*i1 - 2*i7*i2 - 2*i7*i3 + 6*i7*i5 + 2*i7*i6 - 6*sqr(i7) + 4*i8*i1 - 4*i8
*i2 + 2*i8*i3 - 4*i8*i4 - 4*i8*i5 + 8*i8*i6 + 6*i8*i7 - 8*sqr(i8)
=G= -1610;
e5.. 2*i2*i1 - 4*sqr(i1) - 5*sqr(i2) - 6*i3*i1 - 8*sqr(i3) - 2*i4*i1 + 6*i4*i2
- 2*i4*i3 - 6*sqr(i4) - 4*i5*i1 + 2*i5*i2 - 6*i5*i3 - 8*i5*i4 - 7*sqr(i5)
+ 4*i6*i1 - 4*i6*i2 + 6*i6*i3 + 4*i6*i5 - 7*sqr(i6) + 4*i7*i1 - 4*i7*i2
- 4*i7*i3 + 4*i7*i4 + 4*i7*i5 + 4*i7*i6 - 8*sqr(i7) - 2*i8*i1 + 4*i8*i4
+ 2*i8*i6 + 2*i8*i7 - 4*sqr(i8) =G= -1180;
e6.. 2*i2*i1 - 7*sqr(i1) - 7*sqr(i2) - 6*i3*i1 - 2*i3*i2 - 6*sqr(i3) - 2*i4*i1
+ 2*i4*i2 - 2*i4*i3 - 5*sqr(i4) - 2*i5*i1 - 4*i5*i3 + 2*i5*i4 - 5*sqr(i5)
+ 2*i6*i1 - 4*i6*i2 + 4*i6*i3 + 2*i6*i4 + 6*i6*i5 - 9*sqr(i6) + 4*i7*i2
- 4*i7*i3 + 4*i7*i4 - 4*i7*i5 + 8*i7*i6 - 6*sqr(i7) + 4*i8*i1 + 8*i8*i2
+ 2*i8*i3 - 4*i8*i4 - 2*i8*i5 + 4*i8*i6 - 9*sqr(i8) =G= -930;
e7.. (-9*sqr(i1)) - 4*i2*i1 - 8*sqr(i2) + 4*i3*i1 + 2*i3*i2 - 7*sqr(i3) + 4*i4*
i1 + 4*i4*i3 - 7*sqr(i4) - 2*i5*i1 - 12*i5*i2 - 4*i5*i3 - 8*sqr(i5) - 8*i6
*i1 + 2*i6*i2 - 2*i6*i5 - 6*sqr(i6) - 4*i7*i1 - 6*i7*i2 - 2*i7*i3 + 10*i7*
i4 - 2*i7*i5 + 2*i7*i6 - 7*sqr(i7) - 2*i8*i1 + 2*i8*i2 + 2*i8*i3 + 2*i8*i4
- 6*i8*i6 - 2*i8*i7 - 6*sqr(i8) =G= -2790;
e8.. 4*i2*i1 - 7*sqr(i1) - 8*sqr(i2) + 4*i3*i1 - 8*sqr(i3) + 4*i4*i1 + 8*i4*i2
- 6*i4*i3 - 7*sqr(i4) - 2*i5*i2 + 2*i5*i4 - 5*sqr(i5) - 2*i6*i1 - 2*i6*i2
+ 4*i6*i4 - 4*i6*i5 - 7*sqr(i6) - 2*i7*i1 + 8*i7*i2 - 2*i7*i3 - 2*i7*i4
+ 6*i7*i5 + 2*i7*i6 - 7*sqr(i7) + 2*i8*i1 - 6*i8*i2 + 6*i8*i3 + 4*i8*i4
+ 2*i8*i5 - 4*i8*i6 - 6*sqr(i8) =G= -910;
e9.. - (7*sqr(i1) + 6*sqr(i2) + 20.2*i1 - 8.6*i2 + 8*sqr(i3) - 6*i3*i1 + 4*i3*
i2 + 9.4*i3 + 6*sqr(i4) + 2*i4*i1 + 2*i4*i3 - 30.8*i4 + 7*sqr(i5) - 4*i5*
i1 - 2*i5*i2 - 6*i5*i3 - 126.8*i5 + 4*sqr(i6) + 2*i6*i1 - 4*i6*i2 - 4*i6*
i3 - 2*i6*i4 + 6*i6*i5 - 81.4*i6 + 6*sqr(i7) - 2*i7*i1 - 6*i7*i2 - 2*i7*i3
+ 4*i7*i5 + 4*i7*i6 - 94*i7 + 7*sqr(i8) - 4*i8*i1 - 2*i8*i2 + 6*i8*i3 + 4
*i8*i4 - 4*i8*i5 - 2*i8*i6 + 4*i8*i7 - 9.4*i8) + objvar =E= 0;
* set non default bounds
i1.up = 200;
i2.up = 200;
i3.up = 200;
i4.up = 200;
i5.up = 200;
i6.up = 200;
i7.up = 200;
i8.up = 200;
$if set nostart $goto modeldef
* set non default levels
i1.l = 1;
i2.l = 1;
i3.l = 1;
i4.l = 1;
i5.l = 1;
i6.l = 1;
i7.l = 1;
i8.l = 1;
* 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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