MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

Home // Instances // Documentation // Download // Statistics

Instance st_e03

Formatsⓘ	ams gms mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-1161.33660200 p1 ( gdx sol ) (infeas: 2e-09)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-1161.33660400 (ANTIGONE) -1161.33660400 (BARON) -1161.33660200 (COUENNE) -1161.33660200 (LINDO) -1161.33660300 (SCIP)
Referencesⓘ	Bracken, Jerome and McCormick, Garth P, Selected Applications of Nonlinear Programming, John Wiley and Sons, New York, 1968. 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/e03
Added to libraryⓘ	03 Sep 2002
Problem typeⓘ	NLP
#Variablesⓘ	10
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	7
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	quadratic
Objective curvatureⓘ	indefinite
#Nonzeros in Objectiveⓘ	6
#Nonlinear Nonzeros in Objectiveⓘ	2
#Constraintsⓘ	7
#Linear Constraintsⓘ	3
#Quadratic Constraintsⓘ	2
#Polynomial Constraintsⓘ	2
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	21
#Nonlinear Nonzeros in Jacobianⓘ	9
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	13
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	1
#Blocks in Hessian of Lagrangianⓘ	2
Minimal blocksize in Hessian of Lagrangianⓘ	2
Maximal blocksize in Hessian of Lagrangianⓘ	5
Average blocksize in Hessian of Lagrangianⓘ	3.5
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	6.6700e-03
Maximal coefficientⓘ	9.8000e+04
Infeasibility of initial pointⓘ	102
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          8        7        1        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         11       11        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         28       17       11        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,objvar;

Positive Variables  x3,x5;

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


e1..    x1 - 1.22*x4 + x5 =E= 0;

e2..    x9 + 0.222*x10 =E= 35.82;

e3..    3*x7 - x10 =E= 133;

e4.. 0.038*sqr(x8) - 1.098*x8 - 0.325*x6 + x7 =E= 57.425;

e5.. x4*x9*x6 + 1000*x3*x6 - 98000*x3 =E= 0;

e6.. -x1*x8 + x2 + x5 =E= 0;

e7.. 0.13167*x8*x1 + 1.12*x1 - 0.00667*sqr(x8)*x1 - x4 =G= 0;

e8.. 0.063*x4*x7 - 5.04*x1 - 0.035*x2 - 10*x3 - 3.36*x5 + objvar =E= 0;

* set non-default bounds
x1.lo = 1; x1.up = 2000;
x2.lo = 1; x2.up = 16000;
x3.up = 120;
x4.lo = 1; x4.up = 5000;
x5.up = 2000;
x6.lo = 85; x6.up = 93;
x7.lo = 90; x7.up = 95;
x8.lo = 3; x8.up = 12;
x9.lo = 1.2; x9.up = 4;
x10.lo = 145; x10.up = 162;

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;