MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

Home // Instances // Documentation // Download // Statistics


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)
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 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;


Last updated: 2022-05-24 Git hash: 1198c186
Imprint / Privacy Policy / License: CC-BY 4.0