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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex14_1_2

Formatsⓘ	ams gms mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	0.00000000 p1 ( gdx sol ) (infeas: 4e-15)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-0.00000000 (ANTIGONE) 0.00000000 (BARON) -0.00000000 (COUENNE) 0.00000000 (LINDO) 0.00000000 (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. Meintjes, K and Morgan, A P, Chemical-Equilibrium Systems as Numerical Test Problems, ACM Transactions on Mathematical Software, 16:2, 1990, 143-151.
Sourceⓘ	Test Problem ex14.1.2 of Chapter 14 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	NLP
#Variablesⓘ	6
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	4
#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ⓘ	9
#Linear Constraintsⓘ	0
#Quadratic Constraintsⓘ	3
#Polynomial Constraintsⓘ	6
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	41
#Nonlinear Nonzeros in Jacobianⓘ	26
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	9
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	3
#Blocks in Hessian of Lagrangianⓘ	1
Minimal blocksize in Hessian of Lagrangianⓘ	4
Maximal blocksize in Hessian of Lagrangianⓘ	4
Average blocksize in Hessian of Lagrangianⓘ	4.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	4.4975e-07
Maximal coefficientⓘ	4.0000e+01
Infeasibility of initial pointⓘ	0.9999
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         10        2        0        8        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          7        7        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         43       17       26        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,objvar;

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


e1..  - x6 + objvar =E= 0;

e2.. x1*x2 + x1 - 3*x5 =E= 0;

e3.. 2.8845e-6*sqr(x2) + 4.4975e-7*x2 + 2*x1*x2 + x1 + 0.000545176668613029*x2*
     x3 + 3.40735417883143e-5*x2*x4 + sqr(x3)*x2 - 10*x5 - x6 =L= 0;

e4.. (-2.8845e-6*sqr(x2)) - 4.4975e-7*x2 - 2*x1*x2 - x1 - 0.000545176668613029*
     x2*x3 - 3.40735417883143e-5*x2*x4 - sqr(x3)*x2 + 10*x5 - x6 =L= 0;

e5.. 0.386*sqr(x3) + 0.000410621754172864*x3 + 0.000545176668613029*x2*x3 + 2*
     sqr(x3)*x2 - 8*x5 - x6 =L= 0;

e6.. (-0.386*sqr(x3)) - 0.000410621754172864*x3 - 0.000545176668613029*x2*x3 - 
     2*sqr(x3)*x2 + 8*x5 - x6 =L= 0;

e7.. 2*sqr(x4) + 3.40735417883143e-5*x2*x4 - 40*x5 - x6 =L= 0;

e8.. (-2*sqr(x4)) - 3.40735417883143e-5*x2*x4 + 40*x5 - x6 =L= 0;

e9.. 9.615e-7*sqr(x2) + 4.4975e-7*x2 + 0.193*sqr(x3) + 0.000410621754172864*x3
      + sqr(x4) + x1*x2 + x1 + 0.000545176668613029*x2*x3 + 3.40735417883143e-5
     *x2*x4 + sqr(x3)*x2 - x6 =L= 1;

e10.. (-9.615e-7*sqr(x2)) - 4.4975e-7*x2 - 0.193*sqr(x3) - 0.000410621754172864
      *x3 - sqr(x4) - x1*x2 - x1 - 0.000545176668613029*x2*x3 - 
      3.40735417883143e-5*x2*x4 - sqr(x3)*x2 - x6 =L= -1;

* set non-default bounds
x1.lo = 0.0001; x1.up = 100;
x2.lo = 0.0001; x2.up = 100;
x3.lo = 0.0001; x3.up = 100;
x4.lo = 0.0001; x4.up = 100;
x5.lo = 0.0001; x5.up = 100;

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;