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Instance knp3-12
Determining whether 12 3-dimensional spheres of radius 1 can be adjacent to a central sphere of radius 1. This is possible, iff the optimal value of this instance is >= 1.
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 2.18181818 (ANTIGONE) 6.79050187 (BARON) 4.00000000 (COUENNE) 3.31964778 (GUROBI) 6.32680108 (LINDO) 2.62032533 (SCIP) |
| Referencesⓘ | Kucherenko, S, Belotti, P, Liberti, L, and Maculan, N, New formulations for the Kissing Number Problem, Discrete Applied Mathematics, 155:14, 2007, 1837-1841. |
| Sourceⓘ | GAMS Model Library model knp |
| Applicationⓘ | Kissing Number Problem |
| Added to libraryⓘ | 18 Aug 2014 |
| Problem typeⓘ | QCP |
| #Variablesⓘ | 37 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 36 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | max |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 1 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 78 |
| #Linear Constraintsⓘ | 0 |
| #Quadratic Constraintsⓘ | 78 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 498 |
| #Nonlinear Nonzeros in Jacobianⓘ | 432 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 432 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 36 |
| #Blocks in Hessian of Lagrangianⓘ | 3 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 12 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 12 |
| Average blocksize in Hessian of Lagrangianⓘ | 12.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e+00 |
| Maximal coefficientⓘ | 4.0000e+00 |
| Infeasibility of initial pointⓘ | 3.162 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 78 12 66 0 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 37 37 0 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 498 66 432 0
*
* Solve m using NLP maximizing objvar;
Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,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
,objvar;
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,e43,e44,e45,e46,e47,e48,e49,e50,e51,e52,e53
,e54,e55,e56,e57,e58,e59,e60,e61,e62,e63,e64,e65,e66,e67,e68,e69,e70
,e71,e72,e73,e74,e75,e76,e77,e78;
e1.. sqr(x1) + sqr(x2) + sqr(x3) =E= 4;
e2.. sqr(x4) + sqr(x5) + sqr(x6) =E= 4;
e3.. sqr(x7) + sqr(x8) + sqr(x9) =E= 4;
e4.. sqr(x10) + sqr(x11) + sqr(x12) =E= 4;
e5.. sqr(x13) + sqr(x14) + sqr(x15) =E= 4;
e6.. sqr(x16) + sqr(x17) + sqr(x18) =E= 4;
e7.. sqr(x19) + sqr(x20) + sqr(x21) =E= 4;
e8.. sqr(x22) + sqr(x23) + sqr(x24) =E= 4;
e9.. sqr(x25) + sqr(x26) + sqr(x27) =E= 4;
e10.. sqr(x28) + sqr(x29) + sqr(x30) =E= 4;
e11.. sqr(x31) + sqr(x32) + sqr(x33) =E= 4;
e12.. sqr(x34) + sqr(x35) + sqr(x36) =E= 4;
e13.. sqr(x1 - x4) + sqr(x2 - x5) + sqr(x3 - x6) - 4*objvar =G= 0;
e14.. sqr(x1 - x7) + sqr(x2 - x8) + sqr(x3 - x9) - 4*objvar =G= 0;
e15.. sqr(x1 - x10) + sqr(x2 - x11) + sqr(x3 - x12) - 4*objvar =G= 0;
e16.. sqr(x1 - x13) + sqr(x2 - x14) + sqr(x3 - x15) - 4*objvar =G= 0;
e17.. sqr(x1 - x16) + sqr(x2 - x17) + sqr(x3 - x18) - 4*objvar =G= 0;
e18.. sqr(x1 - x19) + sqr(x2 - x20) + sqr(x3 - x21) - 4*objvar =G= 0;
e19.. sqr(x1 - x22) + sqr(x2 - x23) + sqr(x3 - x24) - 4*objvar =G= 0;
e20.. sqr(x1 - x25) + sqr(x2 - x26) + sqr(x3 - x27) - 4*objvar =G= 0;
e21.. sqr(x1 - x28) + sqr(x2 - x29) + sqr(x3 - x30) - 4*objvar =G= 0;
e22.. sqr(x1 - x31) + sqr(x2 - x32) + sqr(x3 - x33) - 4*objvar =G= 0;
e23.. sqr(x1 - x34) + sqr(x2 - x35) + sqr(x3 - x36) - 4*objvar =G= 0;
e24.. sqr(x4 - x7) + sqr(x5 - x8) + sqr(x6 - x9) - 4*objvar =G= 0;
e25.. sqr(x4 - x10) + sqr(x5 - x11) + sqr(x6 - x12) - 4*objvar =G= 0;
e26.. sqr(x4 - x13) + sqr(x5 - x14) + sqr(x6 - x15) - 4*objvar =G= 0;
e27.. sqr(x4 - x16) + sqr(x5 - x17) + sqr(x6 - x18) - 4*objvar =G= 0;
e28.. sqr(x4 - x19) + sqr(x5 - x20) + sqr(x6 - x21) - 4*objvar =G= 0;
e29.. sqr(x4 - x22) + sqr(x5 - x23) + sqr(x6 - x24) - 4*objvar =G= 0;
e30.. sqr(x4 - x25) + sqr(x5 - x26) + sqr(x6 - x27) - 4*objvar =G= 0;
e31.. sqr(x4 - x28) + sqr(x5 - x29) + sqr(x6 - x30) - 4*objvar =G= 0;
e32.. sqr(x4 - x31) + sqr(x5 - x32) + sqr(x6 - x33) - 4*objvar =G= 0;
e33.. sqr(x4 - x34) + sqr(x5 - x35) + sqr(x6 - x36) - 4*objvar =G= 0;
e34.. sqr(x7 - x10) + sqr(x8 - x11) + sqr(x9 - x12) - 4*objvar =G= 0;
e35.. sqr(x7 - x13) + sqr(x8 - x14) + sqr(x9 - x15) - 4*objvar =G= 0;
e36.. sqr(x7 - x16) + sqr(x8 - x17) + sqr(x9 - x18) - 4*objvar =G= 0;
e37.. sqr(x7 - x19) + sqr(x8 - x20) + sqr(x9 - x21) - 4*objvar =G= 0;
e38.. sqr(x7 - x22) + sqr(x8 - x23) + sqr(x9 - x24) - 4*objvar =G= 0;
e39.. sqr(x7 - x25) + sqr(x8 - x26) + sqr(x9 - x27) - 4*objvar =G= 0;
e40.. sqr(x7 - x28) + sqr(x8 - x29) + sqr(x9 - x30) - 4*objvar =G= 0;
e41.. sqr(x7 - x31) + sqr(x8 - x32) + sqr(x9 - x33) - 4*objvar =G= 0;
e42.. sqr(x7 - x34) + sqr(x8 - x35) + sqr(x9 - x36) - 4*objvar =G= 0;
e43.. sqr(x10 - x13) + sqr(x11 - x14) + sqr(x12 - x15) - 4*objvar =G= 0;
e44.. sqr(x10 - x16) + sqr(x11 - x17) + sqr(x12 - x18) - 4*objvar =G= 0;
e45.. sqr(x10 - x19) + sqr(x11 - x20) + sqr(x12 - x21) - 4*objvar =G= 0;
e46.. sqr(x10 - x22) + sqr(x11 - x23) + sqr(x12 - x24) - 4*objvar =G= 0;
e47.. sqr(x10 - x25) + sqr(x11 - x26) + sqr(x12 - x27) - 4*objvar =G= 0;
e48.. sqr(x10 - x28) + sqr(x11 - x29) + sqr(x12 - x30) - 4*objvar =G= 0;
e49.. sqr(x10 - x31) + sqr(x11 - x32) + sqr(x12 - x33) - 4*objvar =G= 0;
e50.. sqr(x10 - x34) + sqr(x11 - x35) + sqr(x12 - x36) - 4*objvar =G= 0;
e51.. sqr(x13 - x16) + sqr(x14 - x17) + sqr(x15 - x18) - 4*objvar =G= 0;
e52.. sqr(x13 - x19) + sqr(x14 - x20) + sqr(x15 - x21) - 4*objvar =G= 0;
e53.. sqr(x13 - x22) + sqr(x14 - x23) + sqr(x15 - x24) - 4*objvar =G= 0;
e54.. sqr(x13 - x25) + sqr(x14 - x26) + sqr(x15 - x27) - 4*objvar =G= 0;
e55.. sqr(x13 - x28) + sqr(x14 - x29) + sqr(x15 - x30) - 4*objvar =G= 0;
e56.. sqr(x13 - x31) + sqr(x14 - x32) + sqr(x15 - x33) - 4*objvar =G= 0;
e57.. sqr(x13 - x34) + sqr(x14 - x35) + sqr(x15 - x36) - 4*objvar =G= 0;
e58.. sqr(x16 - x19) + sqr(x17 - x20) + sqr(x18 - x21) - 4*objvar =G= 0;
e59.. sqr(x16 - x22) + sqr(x17 - x23) + sqr(x18 - x24) - 4*objvar =G= 0;
e60.. sqr(x16 - x25) + sqr(x17 - x26) + sqr(x18 - x27) - 4*objvar =G= 0;
e61.. sqr(x16 - x28) + sqr(x17 - x29) + sqr(x18 - x30) - 4*objvar =G= 0;
e62.. sqr(x16 - x31) + sqr(x17 - x32) + sqr(x18 - x33) - 4*objvar =G= 0;
e63.. sqr(x16 - x34) + sqr(x17 - x35) + sqr(x18 - x36) - 4*objvar =G= 0;
e64.. sqr(x19 - x22) + sqr(x20 - x23) + sqr(x21 - x24) - 4*objvar =G= 0;
e65.. sqr(x19 - x25) + sqr(x20 - x26) + sqr(x21 - x27) - 4*objvar =G= 0;
e66.. sqr(x19 - x28) + sqr(x20 - x29) + sqr(x21 - x30) - 4*objvar =G= 0;
e67.. sqr(x19 - x31) + sqr(x20 - x32) + sqr(x21 - x33) - 4*objvar =G= 0;
e68.. sqr(x19 - x34) + sqr(x20 - x35) + sqr(x21 - x36) - 4*objvar =G= 0;
e69.. sqr(x22 - x25) + sqr(x23 - x26) + sqr(x24 - x27) - 4*objvar =G= 0;
e70.. sqr(x22 - x28) + sqr(x23 - x29) + sqr(x24 - x30) - 4*objvar =G= 0;
e71.. sqr(x22 - x31) + sqr(x23 - x32) + sqr(x24 - x33) - 4*objvar =G= 0;
e72.. sqr(x22 - x34) + sqr(x23 - x35) + sqr(x24 - x36) - 4*objvar =G= 0;
e73.. sqr(x25 - x28) + sqr(x26 - x29) + sqr(x27 - x30) - 4*objvar =G= 0;
e74.. sqr(x25 - x31) + sqr(x26 - x32) + sqr(x27 - x33) - 4*objvar =G= 0;
e75.. sqr(x25 - x34) + sqr(x26 - x35) + sqr(x27 - x36) - 4*objvar =G= 0;
e76.. sqr(x28 - x31) + sqr(x29 - x32) + sqr(x30 - x33) - 4*objvar =G= 0;
e77.. sqr(x28 - x34) + sqr(x29 - x35) + sqr(x30 - x36) - 4*objvar =G= 0;
e78.. sqr(x31 - x34) + sqr(x32 - x35) + sqr(x33 - x36) - 4*objvar =G= 0;
* set non-default bounds
x1.lo = -2; x1.up = 2;
x2.lo = -2; x2.up = 2;
x3.lo = -2; x3.up = 2;
x4.lo = -2; x4.up = 2;
x5.lo = -2; x5.up = 2;
x6.lo = -2; x6.up = 2;
x7.lo = -2; x7.up = 2;
x8.lo = -2; x8.up = 2;
x9.lo = -2; x9.up = 2;
x10.lo = -2; x10.up = 2;
x11.lo = -2; x11.up = 2;
x12.lo = -2; x12.up = 2;
x13.lo = -2; x13.up = 2;
x14.lo = -2; x14.up = 2;
x15.lo = -2; x15.up = 2;
x16.lo = -2; x16.up = 2;
x17.lo = -2; x17.up = 2;
x18.lo = -2; x18.up = 2;
x19.lo = -2; x19.up = 2;
x20.lo = -2; x20.up = 2;
x21.lo = -2; x21.up = 2;
x22.lo = -2; x22.up = 2;
x23.lo = -2; x23.up = 2;
x24.lo = -2; x24.up = 2;
x25.lo = -2; x25.up = 2;
x26.lo = -2; x26.up = 2;
x27.lo = -2; x27.up = 2;
x28.lo = -2; x28.up = 2;
x29.lo = -2; x29.up = 2;
x30.lo = -2; x30.up = 2;
x31.lo = -2; x31.up = 2;
x32.lo = -2; x32.up = 2;
x33.lo = -2; x33.up = 2;
x34.lo = -2; x34.up = 2;
x35.lo = -2; x35.up = 2;
x36.lo = -2; x36.up = 2;
* set non-default levels
x1.l = -1.313011472;
x2.l = 1.373066832;
x3.l = 0.201501424;
x4.l = -0.795448384;
x5.l = -0.831151532;
x6.l = -1.103788532;
x7.l = -0.600677984;
x8.l = 1.425081388;
x9.l = -1.731545108;
x10.l = 0.000842675999999987;
x11.l = 1.992470508;
x12.l = 0.314933512;
x13.l = 1.964532156;
x14.l = 1.049001868;
x15.l = -1.477230068;
x16.l = 0.558875036;
x17.l = -1.361928544;
x18.l = -0.999677868;
x19.l = 0.675714436;
x20.l = -0.258574476;
x21.l = -0.561198936;
x22.l = -0.594234528;
x23.l = -1.47403364;
x24.l = -1.399592848;
x25.l = 0.3564546;
x26.l = 1.323571248;
x27.l = -1.076737048;
x28.l = 0.66293784;
x29.l = 1.103430424;
x30.l = -0.785366092;
x31.l = -1.558030836;
x32.l = 0.00953946399999994;
x33.l = -1.359308952;
x34.l = 1.489849244;
x35.l = -0.93954182;
x36.l = -0.856742712;
Model m / all /;
m.limrow=0; m.limcol=0;
m.tolproj=0.0;
$if NOT '%gams.u1%' == '' $include '%gams.u1%'
$if not set NLP $set NLP NLP
Solve m using %NLP% maximizing objvar;
Last updated: 2024-12-17 Git hash: 8eaceb91