MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex4_1_2

Formatsⓘ	ams gms mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-663.50009660 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-663.50009730 (ANTIGONE) -663.50009730 (BARON) -663.50071840 (COUENNE) -663.50009660 (LINDO) -663.50009720 (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. Moore, R E, Methods and Applications of Interval Analysis, Prentice Hall, Englewood Cliffs, NJ, 1979.
Sourceⓘ	Test Problem ex4.1.2 of Chapter 4 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	NLP
#Variablesⓘ	1
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	1
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	polynomial
Objective curvatureⓘ	nonconvex
#Nonzeros in Objectiveⓘ	1
#Nonlinear Nonzeros in Objectiveⓘ	1
#Constraintsⓘ	0
#Linear Constraintsⓘ	0
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	linear
#Nonzeros in Jacobianⓘ	0
#Nonlinear Nonzeros in Jacobianⓘ	0
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	1
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	1
#Blocks in Hessian of Lagrangianⓘ	1
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ⓘ	1.0638e-01
Maximal coefficientⓘ	5.0000e+02
Infeasibility of initial pointⓘ	0
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          1        1        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          2        2        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*          2        1        1        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,objvar;

Equations  e1;


e1.. -(2.5*sqr(x1) - 500*x1 + 1.666666666*POWER(x1,3) + 1.25*POWER(x1,4) + 
     POWER(x1,5) + 0.8333333*POWER(x1,6) + 0.714285714*POWER(x1,7) + 0.625*
     POWER(x1,8) + 0.555555555*POWER(x1,9) + POWER(x1,10) - 43.6363636*POWER(x1
     ,11) + 0.41666666*POWER(x1,12) + 0.384615384*POWER(x1,13) + 0.357142857*
     POWER(x1,14) + 0.3333333*POWER(x1,15) + 0.3125*POWER(x1,16) + 0.294117647*
     POWER(x1,17) + 0.277777777*POWER(x1,18) + 0.263157894*POWER(x1,19) + 0.25*
     POWER(x1,20) + 0.238095238*POWER(x1,21) + 0.227272727*POWER(x1,22) + 
     0.217391304*POWER(x1,23) + 0.208333333*POWER(x1,24) + 0.2*POWER(x1,25) + 
     0.192307692*POWER(x1,26) + 0.185185185*POWER(x1,27) + 0.178571428*POWER(x1
     ,28) + 0.344827586*POWER(x1,29) + 0.6666666*POWER(x1,30) - 15.48387097*
     POWER(x1,31) + 0.15625*POWER(x1,32) + 0.1515151*POWER(x1,33) + 0.14705882*
     POWER(x1,34) + 0.14285712*POWER(x1,35) + 0.138888888*POWER(x1,36) + 
     0.135135135*POWER(x1,37) + 0.131578947*POWER(x1,38) + 0.128205128*POWER(x1
     ,39) + 0.125*POWER(x1,40) + 0.121951219*POWER(x1,41) + 0.119047619*POWER(
     x1,42) + 0.116279069*POWER(x1,43) + 0.113636363*POWER(x1,44) + 0.1111111*
     POWER(x1,45) + 0.108695652*POWER(x1,46) + 0.106382978*POWER(x1,47) + 
     0.208333333*POWER(x1,48) + 0.408163265*POWER(x1,49) + 0.8*POWER(x1,50))
      + objvar =E= 0;

* set non-default bounds
x1.lo = 1; x1.up = 2;

* set non-default levels
x1.l = 1.0911;

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;