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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance st_e34

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	0.01561953 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	0.01561952 (ANTIGONE) 0.01561953 (BARON) 0.01561953 (COUENNE) 0.01561953 (GUROBI) 0.01561952 (LINDO) 0.01561953 (SCIP)
Referencesⓘ	Hock, W and Schittkowski, K, Test Examples for Nonlinear Programming Codes, Springer Verlag, 1981. Tawarmalani, M and Sahinidis, N V, Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications, Kluwer, 2002.
Sourceⓘ	BARON book instance misc/e34
Added to libraryⓘ	03 Sep 2002
Problem typeⓘ	QCP
#Variablesⓘ	6
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	5
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	linear
Objective curvatureⓘ	linear
#Nonzeros in Objectiveⓘ	6
#Nonlinear Nonzeros in Objectiveⓘ	0
#Constraintsⓘ	4
#Linear Constraintsⓘ	0
#Quadratic Constraintsⓘ	4
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	20
#Nonlinear Nonzeros in Jacobianⓘ	14
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	12
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	0
#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ⓘ	4.3000e+00
Maximal coefficientⓘ	2.6000e+04
Infeasibility of initial pointⓘ	4.97
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          5        1        4        0        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
*         27       13       14        0
*
*  Solve m using NLP minimizing objvar;


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

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

Equations  e1,e2,e3,e4,e5;


e1.. 17.1*x1 - 169*x1*x3 + 204.2*x3 - 3580*x3*x5 + 623.4*x5 - 3810*x4*x6 + 
     212.3*x4 + 1495.5*x6 - 18500*x4*x6 + 38.2*x2 =G= 4.97;

e2.. 17.9*x1 - 139*x1*x3 + 113.9*x3 - 2450*x4*x5 + 169.7*x4 + 337.8*x5 - 16600*
     x4*x6 + 1385.2*x6 - 17200*x5*x6 + 36.8*x2 =G= -1.88;

e3.. 26000*x4*x5 - 70*x4 - 819*x5 - 273*x2 =G= -69.08;

e4.. 159.9*x1 - 14000*x1*x6 + 2198*x6 - 311*x2 + 587*x4 + 391*x5 =G= -118.02;

e5..  - 4.3*x1 - 31.8*x2 - 63.3*x3 - 15.8*x4 - 68.5*x5 - 4.7*x6 + objvar =E= 0;

* set non-default bounds
x1.up = 0.31;
x2.up = 0.046;
x3.up = 0.068;
x4.up = 0.042;
x5.up = 0.028;
x6.up = 0.0134;

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;