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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex8_1_2

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	2.80345848 p1 ( gdx sol ) (infeas: 0) -1.03962661 p2 ( gdx sol ) (infeas: 0) -1.06910879 p3 ( gdx sol ) (infeas: 0) -1.07086102 p4 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-1.11520019 (COUENNE) -1.07086102 (LINDO) -1.07086189 (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. Maranas, C D and Floudas, C A, Global Minimum Potential Energy Conformations of Small Molecules, Journal of Global Optimization, 4:2, 1994, 135-170.
Sourceⓘ	Test Problem ex8.1.2 of Chapter 8 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ⓘ	nonlinear
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ⓘ	cos div power
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ⓘ	2.0944e+00
Maximal coefficientⓘ	6.0080e+05
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;

Positive Variables  x1;

Equations  e1;


e1.. -(588600/POWER(10.8095222429746 - 4.21478541710781*cos((-2.09439333333333)
      + x1),6) - 1079.1/POWER(10.8095222429746 - 4.21478541710781*cos((-
     2.09439333333333) + x1),3) + 600800/POWER(10.8095222429746 - 
     4.21478541710781*cos(x1),6) - 1071.5/POWER(10.8095222429746 - 
     4.21478541710781*cos(x1),3) + 481300/POWER(10.8095222429746 - 
     4.21478541710781*cos(2.09439333333333 + x1),6) - 1064.6/POWER(
     10.8095222429746 - 4.21478541710781*cos(2.09439333333333 + x1),3))
      + objvar =E= 0;

* set non-default bounds
x1.up = 6.28318;

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;