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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)ⓘ
1.10557281 p1 ( gdx sol )
(infeas: 4e-15)
Other points (infeas > 1e-08)ⓘ  
Dual Boundsⓘ
2.18181818 (ANTIGONE)
5.97933462 (BARON)
4. (COUENNE)
2.27696691 (GUROBI)
6.32680108 (LINDO)
2.2806691 (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 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
*         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;
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