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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance st_e36

Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
-246.00000000 p1 ( gdx sol )
(infeas: 0)
Other points (infeas > 1e-08)  
Dual Bounds
-246.00000000 (ANTIGONE)
-246.00000000 (BARON)
-246.00000000 (COUENNE)
-246.00000000 (LINDO)
-246.00000000 (SCIP)
-275.00000000 (SHOT)
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.
Li, Han-Lin and Chou, Chih-Tan, A global approach for nonlinear mixed discrete programming in design optimization, Engineering Optimization, 22:2, 1994, 109-122.
Source BARON book instance misc/e36
Added to library 01 Sep 2002
Problem type MINLP
#Variables 2
#Binary Variables 0
#Integer Variables 1
#Nonlinear Variables 2
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 1
Objective Sense min
Objective type polynomial
Objective curvature nonconcave
#Nonzeros in Objective 2
#Nonlinear Nonzeros in Objective 2
#Constraints 2
#Linear Constraints 0
#Quadratic Constraints 0
#Polynomial Constraints 1
#Signomial Constraints 0
#General Nonlinear Constraints 1
Operands in Gen. Nonlin. Functions exp mul
Constraints curvature indefinite
#Nonzeros in Jacobian 4
#Nonlinear Nonzeros in Jacobian 4
#Nonzeros in (Upper-Left) Hessian of Lagrangian 4
#Nonzeros in Diagonal of Hessian of Lagrangian 2
#Blocks in Hessian of Lagrangian 1
Minimal blocksize in Hessian of Lagrangian 2
Maximal blocksize in Hessian of Lagrangian 2
Average blocksize in Hessian of Lagrangian 2.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 8.0000e-03
Maximal coefficient 1.1000e+01
Infeasibility of initial point 19.2
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
*          3        2        0        1        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          3        2        0        1        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*          7        1        6        0
*
*  Solve m using MINLP minimizing objvar;


Variables  i1,x2,objvar;

Integer Variables  i1;

Equations  e1,e2,e3;


e1.. (-11 + sqr(x2) - 6*x2 + 0.8*i1)*(sqr(3.25*x2 - 0.62*i1) + sqr((-6.35) + 
     0.2*i1 + x2))*(sqr(3.55*x2 - 0.66*i1) + sqr((-6.85) + 0.2*i1 + x2))*(sqr(
     3.6*x2 - 0.7*i1) + sqr((-7.1) + 0.2*i1 + x2))*(sqr(3.8*x2 - 0.82*i1) + 
     sqr((-7.9) + 0.2*i1 + x2)) =E= 0;

e2.. 0.6*i1 - 0.2*x2*i1 + exp((-3) + x2) =L= 1;

e3.. -(2*sqr(x2) + 0.008*POWER(i1,3) - 3.2*x2*i1 - 2*i1) + objvar =E= 0;

* set non-default bounds
i1.lo = 15; i1.up = 25;
x2.lo = 3; x2.up = 5.5;

Model m / all /;

m.limrow=0; m.limcol=0;
m.tolproj=0.0;

$if NOT '%gams.u1%' == '' $include '%gams.u1%'

$if not set MINLP $set MINLP MINLP
Solve m using %MINLP% minimizing objvar;


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