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Instance: himmel11

Formats ams gms lp mod nl osil pip
Primal Bounds
-30665.53867000 p1 ( gdx sol )
(infeas: 2e-15)
Dual Bounds
-30665.54004000 (ANTIGONE)
-30665.53905000 (BARON)
-30665.53907000 (COUENNE)
-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
Infeasibility of initial point 91.79
Sparsity Jacobian Sparsity of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of 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;


Last updated: 2018-09-14 Git hash: ac5a5314
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