OET2.SIF

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* SET UP THE INITIAL DATA *
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NAME          OET2

*   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 x2)
 
*   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-3-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

 R- DIFF      UPPER                    LOWER
 RI RM        M
 R/ H         DIFF                     RM

VARIABLES

    U
    X1
    X2

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  OET2      LO(I)                    -1/1+W
 Z  OET2      UP(I)                    1/1+W
 ND

BOUNDS

 FR OET2      '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                        X2
 ZP E(1,I)    W                        W

 ND

GROUP USES

 DO I         0                        M
 XE LO(I)     E(1,I)    -1.0
 XE UP(I)     E(1,I)
 ND

ENDATA

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* SET UP THE FUNCTION *
* AND RANGE ROUTINES  *
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ELEMENTS      OET2

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