MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex3_1_2

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-30665.53867000 p1 ( gdx sol ) (infeas: 3e-12)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-30665.53986000 (ANTIGONE) -30665.53872000 (BARON) -30665.53899000 (COUENNE) -30665.53870000 (GUROBI) -30665.53869000 (LINDO) -30665.53867000 (SCIP)
Referencesⓘ	Floudas, C A, Pardalos, Panos M, Adjiman, C S, Esposito, W R, Gumus, Zeynep H, Harding, S T, Klepeis, John L, Meyer, Clifford A, and Schweiger, C A, Handbook of Test Problems in Local and Global Optimization, Kluwer Academic Publishers, 1999. Colville, A R, A Comparative Study of Nonlinear Programming Codes. In Kuhn, H W, Ed, Princeton Symposium on Mathematical Programming, Princeton Univ. Press, 1970.
Sourceⓘ	Test Problem ex3.1.2 of Chapter 3 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	QCQP
#Variablesⓘ	5
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	5
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	quadratic
Objective curvatureⓘ	indefinite
#Nonzeros in Objectiveⓘ	3
#Nonlinear Nonzeros in Objectiveⓘ	3
#Constraintsⓘ	6
#Linear Constraintsⓘ	0
#Quadratic Constraintsⓘ	6
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	26
#Nonlinear Nonzeros in Jacobianⓘ	26
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	15
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	1
#Blocks in Hessian of Lagrangianⓘ	1
Minimal blocksize in Hessian of Lagrangianⓘ	5
Maximal blocksize in Hessian of Lagrangianⓘ	5
Average blocksize in Hessian of Lagrangianⓘ	5.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	6.2620e-04
Maximal coefficientⓘ	3.7293e+01
Infeasibility of initial pointⓘ	0
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          7        1        0        6        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          6        6        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         30        1       29        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,objvar;

Equations  e1,e2,e3,e4,e5,e6,e7;


e1.. -(0.8356891*x1*x5 + 37.293239*x1 + 5.3578547*x3*x3) + objvar
      =E= -40792.141;

e2.. 0.0056858*x2*x5 - 0.0022053*x3*x5 + 0.0006262*x1*x4 =L= 6.665593;

e3.. 0.0022053*x3*x5 - 0.0056858*x2*x5 - 0.0006262*x1*x4 =L= 85.334407;

e4.. 0.0071317*x2*x5 + 0.0021813*x3*x3 + 0.0029955*x1*x2 =L= 29.48751;

e5.. (-0.0071317*x2*x5) - 0.0021813*x3*x3 - 0.0029955*x1*x2 =L= -9.48751;

e6.. 0.0047026*x3*x5 + 0.0019085*x3*x4 + 0.0012547*x1*x3 =L= 15.599039;

e7.. (-0.0047026*x3*x5) - 0.0019085*x3*x4 - 0.0012547*x1*x3 =L= -10.699039;

* set non-default bounds
x1.lo = 78; x1.up = 102;
x2.lo = 33; x2.up = 45;
x3.lo = 27; x3.up = 45;
x4.lo = 27; x4.up = 45;
x5.lo = 27; x5.up = 45;

* set non-default levels
x3.l = 29.9953;
x4.l = 45;
x5.l = 36.7758;

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;