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OET3.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME OET3
* 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 = [0,1]
* phi(x,w) = sin(w) - (x1 + x2 w + x3 w^2 )
* Source: K. Oettershagen
* "Ein superlinear konvergenter algorithmus zur losung
* semi-infiniter optimierungsproblem",
* Ph.D thesis, Bonn University, 1982
* SIF input: Nick Gould, February, 1994.
* classification LLR2-AN-4-V
* Discretization
*IE M 2
*IE M 100
IE M 500
* Define the interval
RE LOWER 0.0
RE UPPER 1.0
* Define constants
IE 0 0
R- DIFF UPPER LOWER
RI RM M
R/ H DIFF RM
VARIABLES
U
X1
X2
X3
GROUPS
N OBJ U 1.0
DO I 0 M
RI RI I
R* W RI H
R+ W W LOWER
RM -W W -1.0
R* W**2 W W
RM -W**2 W**2 -1.0
XG LO(I) U 1.0 X1 -1.0
ZG LO(I) X2 -W
ZG LO(I) X3 -W**2
XG UP(I) U 1.0 X1 1.0
ZG UP(I) X2 W
ZG UP(I) X3 W**2
ND
CONSTANTS
DO I 0 M
RI RI I
R* W RI H
R+ W W LOWER
R( SINW SIN W
RM -SINW SINW -1.0
Z OET3 LO(I) -SINW
Z OET3 UP(I) SINW
ND
BOUNDS
FR OET3 'DEFAULT'
ENDATA