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Instance pointpack02

Find the maximum radius of 2 non-overlapping circles that all lie in the unix-box.
Formats ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
1.00000000 p1 ( gdx sol )
(infeas: 0)
1.99999999 p2 ( gdx sol )
(infeas: 0)
Other points (infeas > 1e-08)  
Dual Bounds
2.00000000 (ANTIGONE)
2.00000000 (BARON)
2.00000000 (COUENNE)
2.00000000 (GUROBI)
2.00000000 (LINDO)
2.00000008 (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_02.gms
Application Geometry
Added to library 15 Aug 2014
Problem type QCP
#Variables 5
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 4
#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 3
#Linear Constraints 2
#Quadratic Constraints 1
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature concave
#Nonzeros in Jacobian 9
#Nonlinear Nonzeros in Jacobian 4
#Nonzeros in (Upper-Left) Hessian of Lagrangian 8
#Nonzeros in Diagonal of Hessian of Lagrangian 4
#Blocks in Hessian of Lagrangian 2
Minimal blocksize in Hessian of Lagrangian 2
Maximal blocksize in Hessian of Lagrangian 2
Average blocksize in Hessian of Lagrangian 2.0
#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 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
*          3        0        0        3        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          5        5        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*          9        5        4        0
*
*  Solve m using NLP maximizing objvar;


Variables  x1,x2,x3,x4,objvar;

Positive Variables  x2,x3,x4;

Equations  e1,e2,e3;


e1.. 2*x1*x2 - x1*x1 - x2*x2 - x3*x3 + 2*x3*x4 - x4*x4 + objvar =L= 0;

e2..  - x3 + x4 =L= 0;

e3..  - x1 + x2 =L= 0;

* set non-default bounds
x1.lo = 0.5; x1.up = 1;
x2.up = 1;
x3.up = 1;
x4.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: 2022-08-11 Git hash: f176bd52
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