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OET6.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME OET6
* Problem :
* *********
* A nonlinear programming formulation of a discretization of
* a nonlinear Chebychev problem.
* The problem is
* min max || phi(x,w) ||, for all w in the interval I.
* x w
* I is discretized, and the problem solved over the
* discrete points.
* Nonlinear programming formulation
*
* min u s.t. u - phi >= 0, u + phi >= 0
* x,u
* Specific problem: I = [-0.5,0.5]
* phi(x,w) = 1/1+w - x1 exp(w x3) - x2 exp(w x4)
* Source: K. Oettershagen
* "Ein superlinear knonvergenter algorithmus zur losung
* semi-infiniter optimierungsproblem",
* Ph.D thesis, Bonn University, 1982
* SIF input: Nick Gould, February, 1994.
* classification LOR2-AN-5-V
* Discretization
*IE M 2
*IE M 100
IE M 500
* Define the interval
RE LOWER -0.5
RE UPPER 0.5
* Define constants
IE 0 0
IE 1 1
IE 2 2
R- DIFF UPPER LOWER
RI RM M
R/ H DIFF RM
VARIABLES
U
X1
X2
X3
X4
GROUPS
N OBJ U 1.0
DO I 0 M
XG LO(I) U 1.0
XG UP(I) U 1.0
ND
CONSTANTS
DO I 0 M
RI RI I
R* W RI H
R+ W W LOWER
RA 1+W W 1.0
RD 1/1+W 1+W 1.0
RM -1/1+W 1/1+W -1.0
Z OET6 LO(I) -1/1+W
Z OET6 UP(I) 1/1+W
ND
BOUNDS
FR OET6 'DEFAULT'
ELEMENT TYPE
EV XEYW X Y
EP XEYW W
ELEMENT USES
DO I 0 M
RI RI I
R* W RI H
R+ W W LOWER
XT E(1,I) XEYW
ZV E(1,I) X X1
ZV E(1,I) Y X3
ZP E(1,I) W W
XT E(2,I) XEYW
ZV E(2,I) X X2
ZV E(2,I) Y X4
ZP E(2,I) W W
ND
GROUP USES
DO I 0 M
XE LO(I) E(1,I) -1.0
XE LO(I) E(2,I) -1.0
XE UP(I) E(1,I)
XE UP(I) E(2,I)
ND
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS OET6
TEMPORARIES
R EYW
M EXP
INDIVIDUALS
T XEYW
A EYW EXP( Y * W )
F X * EYW
G X EYW
G Y X * W * EYW
H X Y W * EYW
H Y Y X * W * W * EYW
ENDATA