MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance himmel11

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-30665.53867000 p1 ( gdx sol ) (infeas: 2e-15)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-30665.54004000 (ANTIGONE) -30665.53871000 (BARON) -30665.53907000 (COUENNE) -30665.53867000 (GUROBI) -30665.53868000 (LINDO) -30665.53868000 (SCIP)
Referencesⓘ	Himmelblau, D M, Problem Number 11. In Himmelblau, D M, Applied Nonlinear Programming, Mc Graw Hill, New York, 1972.
Sourceⓘ	GAMS Model Library model himmel11
Applicationⓘ	Test Problem
Added to libraryⓘ	18 Aug 2014
Problem typeⓘ	QCQP
#Variablesⓘ	9
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	5
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	quadratic
Objective curvatureⓘ	indefinite
#Nonzeros in Objectiveⓘ	4
#Nonlinear Nonzeros in Objectiveⓘ	3
#Constraintsⓘ	4
#Linear Constraintsⓘ	1
#Quadratic Constraintsⓘ	3
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	22
#Nonlinear Nonzeros in Jacobianⓘ	13
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	15
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	1
#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ⓘ	6.2620e-04
Maximal coefficientⓘ	5.0000e+03
Infeasibility of initial pointⓘ	91.79
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          5        4        1        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         10       10        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         27       11       16        0
*
*  Solve m using NLP minimizing objvar;


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

Positive Variables  x1,x4;

Equations  e1,e2,e3,e4,e5;


e1..    5*x4 - x5 + 7*x7 - x9 =G= 0;

e2.. -(0.0056858*x6*x9 + 0.0006262*x5*x8 - 0.0022053*x7*x9) + x1 + 2*x4
      =E= 85.334407;

e3.. -(0.0071317*x6*x9 + 0.0029955*x5*x6 + 0.0021813*sqr(x7)) + x2 =E= 80.51249
     ;

e4.. -(0.0047026*x7*x9 + 0.0012547*x5*x7 + 0.0019085*x7*x8) + x3 + 4*x4
      =E= 9.300961;

e5.. -(5.3578547*sqr(x7) + 0.8356891*x5*x9 + 37.293239*x5) - 5000*x4 + objvar
      =E= -40792.141;

* set non-default bounds
x1.up = 92;
x2.lo = 90; x2.up = 110;
x3.lo = 20; x3.up = 25;
x5.lo = 78; x5.up = 102;
x6.lo = 33; x6.up = 45;
x7.lo = 27; x7.up = 45;
x8.lo = 27; x8.up = 45;
x9.lo = 27; x9.up = 45;

* set non-default levels
x5.l = 78.62;
x6.l = 33.44;
x7.l = 31.07;
x8.l = 44.18;
x9.l = 35.22;

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;