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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance fct

Formatsⓘ	ams gms
Primal Bounds (infeas ≤ 1e-08)ⓘ	46.53643357 p1 ( gdx sol ) (infeas: 4e-15) 0.00000000 p2 ( gdx sol ) (infeas: 1e-27)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	0.00000000 (LINDO)
Referencesⓘ	Pinter, J D, LGO - A Model Development System for Continuous Global Optimization, User's Guide, Pinter Consulting Services, Halifax, NS, Canada, Revised edition, 2003.
Sourceⓘ	GAMS Model Library model fct
Applicationⓘ	Test Problem
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	NLP
#Variablesⓘ	11
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	7
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	linear
Objective curvatureⓘ	linear
#Nonzeros in Objectiveⓘ	2
#Nonlinear Nonzeros in Objectiveⓘ	0
#Constraintsⓘ	9
#Linear Constraintsⓘ	2
#Quadratic Constraintsⓘ	4
#Polynomial Constraintsⓘ	1
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	2
Operands in Gen. Nonlin. Functionsⓘ	abs mod sin
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	40
#Nonlinear Nonzeros in Jacobianⓘ	26
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	27
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	7
#Blocks in Hessian of Lagrangianⓘ	3
Minimal blocksize in Hessian of Lagrangianⓘ	1
Maximal blocksize in Hessian of Lagrangianⓘ	5
Average blocksize in Hessian of Lagrangianⓘ	2.333333
#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ⓘ	20
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         10       10        0        0        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      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         43       17       26        0
*
*  Solve m using DNLP minimizing objvar;


Variables  objvar,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12;

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


e1..    objvar - 2*x6 - x7 =E= 0;

e2.. -(sqr(x8) + sqr(x9) + sqr(x10) + sqr(x11) + sqr(x12)) + x7 =E= 0;

e3..  - x3 - x5 + x6 =E= 0;

e4.. -(sqr(sqr(x8) - x9) + sqr(x10) + 2*sqr(x11) + sqr(x12 - x9)) + x2 =E= 0;

e5.. -abs(sin(4*mod(x2,3.14159265358979))) + x3 =E= 0;

e6.. -(sqr(x8 + x9 - x10 + x11 - x12) + 2*sqr(x9 - x8 + x10 - x11 + x12)) + x4
      =E= 0;

e7.. -abs(sin(3*mod(x4,3.14159265358979))) + x5 =E= 0;

e8.. 3*sqr(x9) + sqr(x10) - 2*sqr(x11) + sqr(x12) + x8 =E= 0;

e9..    x8 + 4*x9 - x10 + x11 - 3*x12 =E= 0;

e10.. sqr(x8) - sqr(x10) + 2*sqr(x9) - sqr(x11) - sqr(x12) =E= 0;

* set non-default bounds
x8.lo = -10; x8.up = 5;
x9.lo = -10; x9.up = 5;
x10.lo = -10; x10.up = 5;
x11.lo = -10; x11.up = 5;
x12.lo = -10; x12.up = 5;

* set non-default levels
x8.l = 2;
x9.l = 2;
x10.l = 2;
x11.l = 2;
x12.l = 2;

Model m / all /;

m.limrow=0; m.limcol=0;
m.tolproj=0.0;

$if NOT '%gams.u1%' == '' $include '%gams.u1%'

$if not set DNLP $set DNLP DNLP
Solve m using %DNLP% minimizing objvar;