MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Removed Instance circle

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	4.57424778 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	4.57424778 (ANTIGONE) 4.57424778 (BARON) 4.57424778 (COUENNE) 4.57424778 (GUROBI) 4.57424778 (LINDO) 4.57424774 (SCIP)
Referencesⓘ	Gill, Philip E, Murray, Walter, Saunders, M A, Drud, Arne S, and Kalvelagen, Erwin, GAMS/SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization, 2002.
Sourceⓘ	GAMS Model Library model circle
Applicationⓘ	Geometry
Added to libraryⓘ	31 Jul 2001
Removed from libraryⓘ	16 Feb 2022
Removed becauseⓘ	Instance is continuous and easily recognized as SOCP
Problem typeⓘ	QCP
#Variablesⓘ	3
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	3
#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ⓘ	10
#Linear Constraintsⓘ	0
#Quadratic Constraintsⓘ	10
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	30
#Nonlinear Nonzeros in Jacobianⓘ	30
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	3
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	3
#Blocks in Hessian of Lagrangianⓘ	3
Minimal blocksize in Hessian of Lagrangianⓘ	1
Maximal blocksize in Hessian of Lagrangianⓘ	1
Average blocksize in Hessian of Lagrangianⓘ	1.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	1.0000e+00
Maximal coefficientⓘ	9.9831e+00
Infeasibility of initial pointⓘ	0
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         10        0        0       10        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          3        3        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         30        0       30        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,objvar;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10;


e1.. sqr(2.545724188 - x1) + sqr(9.983058643 - x2) - sqr(objvar) =L= 0;

e2.. sqr(8.589400372 - x1) + sqr(6.208600402 - x2) - sqr(objvar) =L= 0;

e3.. sqr(5.953378204 - x1) + sqr(9.920197351 - x2) - sqr(objvar) =L= 0;

e4.. sqr(3.710241136 - x1) + sqr(7.860254203 - x2) - sqr(objvar) =L= 0;

e5.. sqr(3.629909053 - x1) + sqr(2.176232347 - x2) - sqr(objvar) =L= 0;

e6.. sqr(3.016475803 - x1) + sqr(6.757468831 - x2) - sqr(objvar) =L= 0;

e7.. sqr(4.148474536 - x1) + sqr(2.435660776 - x2) - sqr(objvar) =L= 0;

e8.. sqr(8.706433123 - x1) + sqr(3.250724797 - x2) - sqr(objvar) =L= 0;

e9.. sqr(1.604023507 - x1) + sqr(7.020357481 - x2) - sqr(objvar) =L= 0;

e10.. sqr(5.501896021 - x1) + sqr(4.918207429 - x2) - sqr(objvar) =L= 0;

* set non-default bounds
objvar.lo = 0;

* set non-default levels
x1.l = 5.155228315;
x2.l = 5.793541075;
objvar.l = 5.49209550544626;

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;