MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance pointpack12
Find the maximum radius of 12 non-overlapping circles that all lie in the unix-box.
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 0.22686275 (ANTIGONE) 0.23870267 (BARON) 0.41121776 (COUENNE) 0.15111262 (GUROBI) 0.39980360 (LINDO) 0.18957657 (SCIP) |
| Referencesⓘ | Anstreicher, Kurt, Semidefinite programming versus the reformulation-linearization technique for nonconvex quadratically constrained quadratic programming, Journal of Global Optimization, 43:2, 2009, 471-484. |
| Sourceⓘ | ANTIGONE test library model Other_MIQCQP/pnt_pack_12.gms |
| Applicationⓘ | Geometry |
| Added to libraryⓘ | 15 Aug 2014 |
| Problem typeⓘ | QCP |
| #Variablesⓘ | 25 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 24 |
| #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ⓘ | 12 |
| #Quadratic Constraintsⓘ | 66 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | concave |
| #Nonzeros in Jacobianⓘ | 354 |
| #Nonlinear Nonzeros in Jacobianⓘ | 264 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 288 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 24 |
| #Blocks in Hessian of Lagrangianⓘ | 2 |
| 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ⓘ | 2.0000e+00 |
| Infeasibility of initial pointⓘ | 0 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 78 0 0 78 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 25 25 0 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 354 90 264 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,objvar;
Positive Variables x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,x20,x21
,x22,x23,x24;
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.. 2*x1*x2 - x1*x1 - x2*x2 - x13*x13 + 2*x13*x14 - x14*x14 + objvar =L= 0;
e2.. 2*x1*x3 - x1*x1 - x3*x3 - x13*x13 + 2*x13*x15 - x15*x15 + objvar =L= 0;
e3.. 2*x1*x4 - x1*x1 - x4*x4 - x13*x13 + 2*x13*x16 - x16*x16 + objvar =L= 0;
e4.. 2*x1*x5 - x1*x1 - x5*x5 - x13*x13 + 2*x13*x17 - x17*x17 + objvar =L= 0;
e5.. 2*x1*x6 - x1*x1 - x6*x6 - x13*x13 + 2*x13*x18 - x18*x18 + objvar =L= 0;
e6.. 2*x1*x7 - x1*x1 - x7*x7 - x13*x13 + 2*x13*x19 - x19*x19 + objvar =L= 0;
e7.. 2*x1*x8 - x1*x1 - x8*x8 - x13*x13 + 2*x13*x20 - x20*x20 + objvar =L= 0;
e8.. 2*x1*x9 - x1*x1 - x9*x9 - x13*x13 + 2*x13*x21 - x21*x21 + objvar =L= 0;
e9.. 2*x1*x10 - x1*x1 - x10*x10 - x13*x13 + 2*x13*x22 - x22*x22 + objvar =L= 0;
e10.. 2*x1*x11 - x1*x1 - x11*x11 - x13*x13 + 2*x13*x23 - x23*x23 + objvar =L= 0
;
e11.. 2*x1*x12 - x1*x1 - x12*x12 - x13*x13 + 2*x13*x24 - x24*x24 + objvar =L= 0
;
e12.. 2*x2*x3 - x2*x2 - x3*x3 - x14*x14 + 2*x14*x15 - x15*x15 + objvar =L= 0;
e13.. 2*x2*x4 - x2*x2 - x4*x4 - x14*x14 + 2*x14*x16 - x16*x16 + objvar =L= 0;
e14.. 2*x2*x5 - x2*x2 - x5*x5 - x14*x14 + 2*x14*x17 - x17*x17 + objvar =L= 0;
e15.. 2*x2*x6 - x2*x2 - x6*x6 - x14*x14 + 2*x14*x18 - x18*x18 + objvar =L= 0;
e16.. 2*x2*x7 - x2*x2 - x7*x7 - x14*x14 + 2*x14*x19 - x19*x19 + objvar =L= 0;
e17.. 2*x2*x8 - x2*x2 - x8*x8 - x14*x14 + 2*x14*x20 - x20*x20 + objvar =L= 0;
e18.. 2*x2*x9 - x2*x2 - x9*x9 - x14*x14 + 2*x14*x21 - x21*x21 + objvar =L= 0;
e19.. 2*x2*x10 - x2*x2 - x10*x10 - x14*x14 + 2*x14*x22 - x22*x22 + objvar =L= 0
;
e20.. 2*x2*x11 - x2*x2 - x11*x11 - x14*x14 + 2*x14*x23 - x23*x23 + objvar =L= 0
;
e21.. 2*x2*x12 - x2*x2 - x12*x12 - x14*x14 + 2*x14*x24 - x24*x24 + objvar =L= 0
;
e22.. 2*x3*x4 - x3*x3 - x4*x4 - x15*x15 + 2*x15*x16 - x16*x16 + objvar =L= 0;
e23.. 2*x3*x5 - x3*x3 - x5*x5 - x15*x15 + 2*x15*x17 - x17*x17 + objvar =L= 0;
e24.. 2*x3*x6 - x3*x3 - x6*x6 - x15*x15 + 2*x15*x18 - x18*x18 + objvar =L= 0;
e25.. 2*x3*x7 - x3*x3 - x7*x7 - x15*x15 + 2*x15*x19 - x19*x19 + objvar =L= 0;
e26.. 2*x3*x8 - x3*x3 - x8*x8 - x15*x15 + 2*x15*x20 - x20*x20 + objvar =L= 0;
e27.. 2*x3*x9 - x3*x3 - x9*x9 - x15*x15 + 2*x15*x21 - x21*x21 + objvar =L= 0;
e28.. 2*x3*x10 - x3*x3 - x10*x10 - x15*x15 + 2*x15*x22 - x22*x22 + objvar =L= 0
;
e29.. 2*x3*x11 - x3*x3 - x11*x11 - x15*x15 + 2*x15*x23 - x23*x23 + objvar =L= 0
;
e30.. 2*x3*x12 - x3*x3 - x12*x12 - x15*x15 + 2*x15*x24 - x24*x24 + objvar =L= 0
;
e31.. 2*x4*x5 - x4*x4 - x5*x5 - x16*x16 + 2*x16*x17 - x17*x17 + objvar =L= 0;
e32.. 2*x4*x6 - x4*x4 - x6*x6 - x16*x16 + 2*x16*x18 - x18*x18 + objvar =L= 0;
e33.. 2*x4*x7 - x4*x4 - x7*x7 - x16*x16 + 2*x16*x19 - x19*x19 + objvar =L= 0;
e34.. 2*x4*x8 - x4*x4 - x8*x8 - x16*x16 + 2*x16*x20 - x20*x20 + objvar =L= 0;
e35.. 2*x4*x9 - x4*x4 - x9*x9 - x16*x16 + 2*x16*x21 - x21*x21 + objvar =L= 0;
e36.. 2*x4*x10 - x4*x4 - x10*x10 - x16*x16 + 2*x16*x22 - x22*x22 + objvar =L= 0
;
e37.. 2*x4*x11 - x4*x4 - x11*x11 - x16*x16 + 2*x16*x23 - x23*x23 + objvar =L= 0
;
e38.. 2*x4*x12 - x4*x4 - x12*x12 - x16*x16 + 2*x16*x24 - x24*x24 + objvar =L= 0
;
e39.. 2*x5*x6 - x5*x5 - x6*x6 - x17*x17 + 2*x17*x18 - x18*x18 + objvar =L= 0;
e40.. 2*x5*x7 - x5*x5 - x7*x7 - x17*x17 + 2*x17*x19 - x19*x19 + objvar =L= 0;
e41.. 2*x5*x8 - x5*x5 - x8*x8 - x17*x17 + 2*x17*x20 - x20*x20 + objvar =L= 0;
e42.. 2*x5*x9 - x5*x5 - x9*x9 - x17*x17 + 2*x17*x21 - x21*x21 + objvar =L= 0;
e43.. 2*x5*x10 - x5*x5 - x10*x10 - x17*x17 + 2*x17*x22 - x22*x22 + objvar =L= 0
;
e44.. 2*x5*x11 - x5*x5 - x11*x11 - x17*x17 + 2*x17*x23 - x23*x23 + objvar =L= 0
;
e45.. 2*x5*x12 - x5*x5 - x12*x12 - x17*x17 + 2*x17*x24 - x24*x24 + objvar =L= 0
;
e46.. 2*x6*x7 - x6*x6 - x7*x7 - x18*x18 + 2*x18*x19 - x19*x19 + objvar =L= 0;
e47.. 2*x6*x8 - x6*x6 - x8*x8 - x18*x18 + 2*x18*x20 - x20*x20 + objvar =L= 0;
e48.. 2*x6*x9 - x6*x6 - x9*x9 - x18*x18 + 2*x18*x21 - x21*x21 + objvar =L= 0;
e49.. 2*x6*x10 - x6*x6 - x10*x10 - x18*x18 + 2*x18*x22 - x22*x22 + objvar =L= 0
;
e50.. 2*x6*x11 - x6*x6 - x11*x11 - x18*x18 + 2*x18*x23 - x23*x23 + objvar =L= 0
;
e51.. 2*x6*x12 - x6*x6 - x12*x12 - x18*x18 + 2*x18*x24 - x24*x24 + objvar =L= 0
;
e52.. 2*x7*x8 - x7*x7 - x8*x8 - x19*x19 + 2*x19*x20 - x20*x20 + objvar =L= 0;
e53.. 2*x7*x9 - x7*x7 - x9*x9 - x19*x19 + 2*x19*x21 - x21*x21 + objvar =L= 0;
e54.. 2*x7*x10 - x7*x7 - x10*x10 - x19*x19 + 2*x19*x22 - x22*x22 + objvar =L= 0
;
e55.. 2*x7*x11 - x7*x7 - x11*x11 - x19*x19 + 2*x19*x23 - x23*x23 + objvar =L= 0
;
e56.. 2*x7*x12 - x7*x7 - x12*x12 - x19*x19 + 2*x19*x24 - x24*x24 + objvar =L= 0
;
e57.. 2*x8*x9 - x8*x8 - x9*x9 - x20*x20 + 2*x20*x21 - x21*x21 + objvar =L= 0;
e58.. 2*x8*x10 - x8*x8 - x10*x10 - x20*x20 + 2*x20*x22 - x22*x22 + objvar =L= 0
;
e59.. 2*x8*x11 - x8*x8 - x11*x11 - x20*x20 + 2*x20*x23 - x23*x23 + objvar =L= 0
;
e60.. 2*x8*x12 - x8*x8 - x12*x12 - x20*x20 + 2*x20*x24 - x24*x24 + objvar =L= 0
;
e61.. 2*x9*x10 - x9*x9 - x10*x10 - x21*x21 + 2*x21*x22 - x22*x22 + objvar =L= 0
;
e62.. 2*x9*x11 - x9*x9 - x11*x11 - x21*x21 + 2*x21*x23 - x23*x23 + objvar =L= 0
;
e63.. 2*x9*x12 - x9*x9 - x12*x12 - x21*x21 + 2*x21*x24 - x24*x24 + objvar =L= 0
;
e64.. 2*x10*x11 - x10*x10 - x11*x11 - x22*x22 + 2*x22*x23 - x23*x23 + objvar
=L= 0;
e65.. 2*x10*x12 - x10*x10 - x12*x12 - x22*x22 + 2*x22*x24 - x24*x24 + objvar
=L= 0;
e66.. 2*x11*x12 - x11*x11 - x12*x12 - x23*x23 + 2*x23*x24 - x24*x24 + objvar
=L= 0;
e67.. - x13 + x14 =L= 0;
e68.. - x1 + x2 =L= 0;
e69.. - x2 + x3 =L= 0;
e70.. - x3 + x4 =L= 0;
e71.. - x4 + x5 =L= 0;
e72.. - x5 + x6 =L= 0;
e73.. - x6 + x7 =L= 0;
e74.. - x7 + x8 =L= 0;
e75.. - x8 + x9 =L= 0;
e76.. - x9 + x10 =L= 0;
e77.. - x10 + x11 =L= 0;
e78.. - x11 + x12 =L= 0;
* set non-default bounds
x1.lo = 0.5; x1.up = 1;
x2.lo = 0.5; x2.up = 1;
x3.lo = 0.5; x3.up = 1;
x4.lo = 0.5; x4.up = 1;
x5.lo = 0.5; x5.up = 1;
x6.lo = 0.5; x6.up = 1;
x7.up = 1;
x8.up = 1;
x9.up = 1;
x10.up = 1;
x11.up = 1;
x12.up = 1;
x13.up = 1;
x14.up = 1;
x15.up = 1;
x16.up = 1;
x17.up = 1;
x18.up = 1;
x19.up = 1;
x20.up = 1;
x21.up = 1;
x22.up = 1;
x23.up = 1;
x24.up = 1;
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: 2025-08-07 Git hash: e62cedfc