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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance st_e37

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	0.97913912 p1 ( gdx sol ) (infeas: 0) 0.00104172 p2 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	0.00104167 (ANTIGONE) 0.00104172 (BARON) 0.00104172 (COUENNE) 0.00104171 (LINDO) 0.00104123 (SCIP)
Referencesⓘ	Tawarmalani, M and Sahinidis, N V, Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications, Kluwer, 2002. Beck, J V and Arnold, K J, Parameter Estimation in Engineering and Science, Wiley, New York, 1977.
Sourceⓘ	BARON book instance misc/e37
Added to libraryⓘ	03 Sep 2002
Problem typeⓘ	NLP
#Variablesⓘ	4
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	4
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	nonlinear
Objective curvatureⓘ	nonconcave
#Nonzeros in Objectiveⓘ	4
#Nonlinear Nonzeros in Objectiveⓘ	4
#Constraintsⓘ	1
#Linear Constraintsⓘ	1
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ	exp mul sqr
Constraints curvatureⓘ	linear
#Nonzeros in Jacobianⓘ	2
#Nonlinear Nonzeros in Jacobianⓘ	0
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	16
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	4
#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ⓘ	1.2700e-02
Maximal coefficientⓘ	1.0000e+01
Infeasibility of initial pointⓘ	0
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          2        1        0        1        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          5        5        0        0        0        0        0        0
*  FX      2
*  
*  Nonzero counts
*      Total    const       NL      DLL
*          7        3        4        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,objvar,x4,x5;

Positive Variables  x1,x2;

Equations  e1,e2;


e1..    x1 - x2 =L= 0;

e2.. -(sqr((-1.9837) + x4 + x5) + sqr((-0.8393) + exp(-x1)*x4 + exp(-x2)*x5) + 
     sqr((-0.4305) + exp(-2*x1)*x4 + exp(-2*x2)*x5) + sqr((-0.2441) + exp(-3*x1
     )*x4 + exp(-3*x2)*x5) + sqr((-0.1248) + exp(-4*x1)*x4 + exp(-4*x2)*x5) + 
     sqr((-0.0981) + exp(-5*x1)*x4 + exp(-5*x2)*x5) + sqr((-0.0549) + exp(-6*x1
     )*x4 + exp(-6*x2)*x5) + sqr((-0.0174) + exp(-7*x1)*x4 + exp(-7*x2)*x5) + 
     sqr((-0.0249) + exp(-8*x1)*x4 + exp(-8*x2)*x5) + sqr((-0.0154) + exp(-9*x1
     )*x4 + exp(-9*x2)*x5) + sqr((-0.0127) + exp(-10*x1)*x4 + exp(-10*x2)*x5))
      + objvar =E= 0;

* set non-default bounds
x1.up = 100;
x2.up = 100;
x4.fx = 1;
x5.fx = 1;

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;