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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance st_e16

Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
12292.46728000 p1 ( gdx sol )
(infeas: 0)
Other points (infeas > 1e-08)  
Dual Bounds
12292.46623000 (ANTIGONE)
12292.46726000 (BARON)
12292.46680000 (COUENNE)
12292.46728000 (LINDO)
12292.46728000 (SCIP)
References Tawarmalani, M and Sahinidis, N V, Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications, Kluwer, 2002.
Floudas, C A and Ciric, A R, Strategies for overcoming uncertainties in heat exchanger network synthesis, Computers and Chemical Engineering, 13:10, 1989, 1133-1152.
Source BARON book instance misc/e16
Added to library 03 Sep 2002
Problem type NLP
#Variables 12
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 8
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type nonlinear
Objective curvature nonconcave
#Nonzeros in Objective 4
#Nonlinear Nonzeros in Objective 4
#Constraints 9
#Linear Constraints 5
#Quadratic Constraints 4
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions div mul vcpower
Constraints curvature indefinite
#Nonzeros in Jacobian 30
#Nonlinear Nonzeros in Jacobian 14
#Nonzeros in (Upper-Left) Hessian of Lagrangian 20
#Nonzeros in Diagonal of Hessian of Lagrangian 4
#Blocks in Hessian of Lagrangian 2
Minimal blocksize in Hessian of Lagrangian 4
Maximal blocksize in Hessian of Lagrangian 4
Average blocksize in Hessian of Lagrangian 4.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 1.6667e-01
Maximal coefficient 5.0000e+03
Infeasibility of initial point 1000
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
*         10       10        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         13       13        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         35       17       18        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,objvar;

Positive Variables  x1,x2,x3,x4,x5,x6,x7,x8;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10;


e1..    x1 + x2 =E= 10;

e2..    x1 - x3 + x6 =E= 0;

e3..    x2 - x4 + x5 =E= 0;

e4..  - x3 + x5 + x7 =E= 0;

e5..  - x4 + x6 + x8 =E= 0;

e6.. x12*x6 - x9*x3 + 100*x1 =E= 0;

e7.. x10*x5 - x11*x4 + 100*x2 =E= 0;

e8.. x3*(x10 - x9) =E= 800;

e9.. x4*(x12 - x11) =E= 1000;

e10.. -(1200*(800/(258.333333333333 + 2.5*(0.666666666666667*((320 - x10)*(300
       - x9))**0.5 - 0.166666666666667*x9 - 0.166666666666667*x10)))**0.6 + 
      1200*(5000/(106.666666666667 + 0.666666666666667*((340 - x12)*(300 - x11)
      )**0.5 - 0.166666666666667*x11 - 0.166666666666667*x12))**0.6) + objvar
       =E= 0;

* set non-default bounds
x1.up = 10;
x2.up = 10;
x3.up = 10;
x4.up = 10;
x5.up = 10;
x6.up = 10;
x7.up = 10;
x8.up = 10;
x9.lo = 100; x9.up = 290;
x10.lo = 100; x10.up = 310;
x11.lo = 100; x11.up = 290;
x12.lo = 100; x12.up = 330;

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;


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