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Instance kall_congruentcircles_c41

A set of circles are to be cut from rectangular design plates to be produced, or from a set of stocked rectangles of known geometric dimensions.
The objective is to minimize the area of the design rectangles.
The design plates are subject to lower and upper bounds of their widths and lengths.
The objects are free of any orientation restrictions.

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	0.85840735 p1 ( gdx sol ) (infeas: 1e-10)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	0.85840682 (ANTIGONE) 0.85840735 (BARON) 0.85840735 (COUENNE) 0.85840666 (GUROBI) 0.85840735 (LINDO) 0.85840734 (SCIP)
Referencesⓘ	Kallrath, Josef, Cutting circles and polygons from area-minimizing rectangles, Journal of Global Optimization, 43:2-3, 2009, 299-328.
Sourceⓘ	ANTIGONE test library model Other_MIQCQP/kall_congruentcircles_c41
Applicationⓘ	Geometry
Added to libraryⓘ	15 Aug 2014
Problem typeⓘ	QCP
#Variablesⓘ	12
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	10
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	linear
Objective curvatureⓘ	linear
#Nonzeros in Objectiveⓘ	1
#Nonlinear Nonzeros in Objectiveⓘ	0
#Constraintsⓘ	24
#Linear Constraintsⓘ	17
#Quadratic Constraintsⓘ	7
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	59
#Nonlinear Nonzeros in Jacobianⓘ	26
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	34
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	8
#Blocks in Hessian of Lagrangianⓘ	3
Minimal blocksize in Hessian of Lagrangianⓘ	2
Maximal blocksize in Hessian of Lagrangianⓘ	4
Average blocksize in Hessian of Lagrangianⓘ	3.333333
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	1.0000e+00
Maximal coefficientⓘ	1.0000e+00
Infeasibility of initial pointⓘ	2.892
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         24        2        6       16        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         12       12        0        0        0        0        0        0
*  FX      4
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         59       33       26        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,objvar;

Positive Variables  x10,x11;

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;


e1..  - x1 + objvar =E= -3.14159265358979;

e2.. -x10*x11 + x1 =E= 0;

e3.. (x2 - x4)*(x2 - x4) + (x3 - x5)*(x3 - x5) =G= 1;

e4.. (x2 - x6)*(x2 - x6) + (x3 - x7)*(x3 - x7) =G= 1;

e5.. (x2 - x8)*(x2 - x8) + (x3 - x9)*(x3 - x9) =G= 1;

e6.. (x4 - x6)*(x4 - x6) + (x5 - x7)*(x5 - x7) =G= 1;

e7.. (x4 - x8)*(x4 - x8) + (x5 - x9)*(x5 - x9) =G= 1;

e8.. (x6 - x8)*(x6 - x8) + (x7 - x9)*(x7 - x9) =G= 1;

e9..    x2 - x10 =L= -0.5;

e10..    x3 - x11 =L= -0.5;

e11..    x4 - x10 =L= -0.5;

e12..    x5 - x11 =L= -0.5;

e13..    x6 - x10 =L= -0.5;

e14..    x7 - x11 =L= -0.5;

e15..    x8 - x10 =L= -0.5;

e16..    x9 - x11 =L= -0.5;

e17..    x2 =L= 2;

e18..    x3 =L= 0.5;

e19..    x2 - x4 =L= 0;

e20..    x2 - x6 =L= 0;

e21..    x2 - x8 =L= 0;

e22..    x4 - x6 =L= 0;

e23..    x4 - x8 =L= 0;

e24..    x6 - x8 =L= 0;

* set non-default bounds
x1.lo = 0.25; x1.up = 4;
x2.lo = 0.5; x2.up = 3.5;
x3.fx = 0.5;
x4.lo = 0.5; x4.up = 3.5;
x5.fx = 0.5;
x6.lo = 0.5; x6.up = 3.5;
x7.fx = 0.5;
x8.lo = 0.5; x8.up = 3.5;
x9.fx = 0.5;
x10.up = 4;
x11.up = 1;
objvar.lo = 0; objvar.up = 4;

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% minimizing objvar;