MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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

Instance himmel16

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-0.8660254 p2 ( gdx sol ) (infeas: 2e-13) -0.67498144 p1 ( gdx sol ) (infeas: 2e-16)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-0.86602541 (ANTIGONE) -0.8660255 (BARON) -0.8660254 (COUENNE) -0.86602687 (GUROBI) -0.8660254 (LINDO) -0.86602547 (SCIP)
Referencesⓘ	Himmelblau, D M, Problem Number 16. In Himmelblau, D M, Applied Nonlinear Programming, Mc Graw Hill, New York, 1972.
Sourceⓘ	GAMS Model Library model himmel16
Applicationⓘ	Geometry
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	QCP
#Variablesⓘ	18
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	12
#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ⓘ	21
#Linear Constraintsⓘ	0
#Quadratic Constraintsⓘ	21
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	90
#Nonlinear Nonzeros in Jacobianⓘ	84
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	96
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	12
#Blocks in Hessian of Lagrangianⓘ	1
Minimal blocksize in Hessian of Lagrangianⓘ	12
Maximal blocksize in Hessian of Lagrangianⓘ	12
Average blocksize in Hessian of Lagrangianⓘ	12.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	5.0000e-01
Maximal coefficientⓘ	1.0000e+00
Infeasibility of initial pointⓘ	0.2
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         22        7        0       15        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         19       19        0        0        0        0        0        0
*  FX      3
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         97       13       84        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18
          ,objvar;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19
          ,e20,e21,e22;


e1.. sqr(x1 - x2) + sqr(x7 - x8) =L= 1;

e2.. sqr(x1 - x3) + sqr(x7 - x9) =L= 1;

e3.. sqr(x1 - x4) + sqr(x7 - x10) =L= 1;

e4.. sqr(x1 - x5) + sqr(x7 - x11) =L= 1;

e5.. sqr(x1 - x6) + sqr(x7 - x12) =L= 1;

e6.. sqr(x2 - x3) + sqr(x8 - x9) =L= 1;

e7.. sqr(x2 - x4) + sqr(x8 - x10) =L= 1;

e8.. sqr(x2 - x5) + sqr(x8 - x11) =L= 1;

e9.. sqr(x2 - x6) + sqr(x8 - x12) =L= 1;

e10.. sqr(x3 - x4) + sqr(x9 - x10) =L= 1;

e11.. sqr(x3 - x5) + sqr(x9 - x11) =L= 1;

e12.. sqr(x3 - x6) + sqr(x9 - x12) =L= 1;

e13.. sqr(x4 - x5) + sqr(x10 - x11) =L= 1;

e14.. sqr(x4 - x6) + sqr(x10 - x12) =L= 1;

e15.. sqr(x5 - x6) + sqr(x11 - x12) =L= 1;

e16..  - x13 - x14 - x15 - x16 - x17 - x18 - objvar =E= 0;

e17.. -0.5*(x1*x8 - x7*x2) + x13 =E= 0;

e18.. -0.5*(x2*x9 - x8*x3) + x14 =E= 0;

e19.. -0.5*(x3*x10 - x9*x4) + x15 =E= 0;

e20.. -0.5*(x4*x11 - x10*x5) + x16 =E= 0;

e21.. -0.5*(x5*x12 - x11*x6) + x17 =E= 0;

e22.. -0.5*(x6*x7 - x12*x1) + x18 =E= 0;

* set non-default bounds
x1.fx = 0;
x7.fx = 0;
x8.fx = 0;

* set non-default levels
x2.l = 0.5;
x3.l = 0.5;
x4.l = 0.5;
x9.l = 0.4;
x10.l = 0.8;
x11.l = 0.8;
x12.l = 0.4;

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;