PT.SIF

***************************
* SET UP THE INITIAL DATA *
***************************

NAME          PT   

*   Problem :
*   *********

*   A nonlinear programming formulation of a discretization of
*   a nonlinear minimax 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
*       x,u

*   Specific problem: I = [0,1]
*   phi(x,w) = (2w^2-1)x + w(1-w)(1-x)
 
*   Source: E. Polak and A. L. Tits,
*   "A recursive quadratic programming algorithm for semi-infinite
*    optimization problems",
*   Appl. Math. Optim. 8, 1982, pp 325-349.

*   SIF input: Nick Gould, February, 1994.

*   classification LLR2-AN-2-V

*   Discretization

*IE M                   2
*IE M                   100
 IE M                   500

*   Define the interval

 RE LOWER               0.0
 RE UPPER               1.0

*   Define constants

 RE ONE                 1.0
 IE 0                   0

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

VARIABLES

    U
    X

GROUPS

 N  OBJ       U         1.0

 DO I         0                        M
 RI RI        I
 R* W         RI                       H
 R+ W         W                        LOWER

 RS 1-W       W         1.0
 R* W(1-W)    W                        1-W
 R* W**2      W                        W
 RM 2W**2     W**2      2.0
 R- 2W**2-1   2W**2                    ONE
 R- XCOEFF    W(1-W)                   2W**2-1
 
 XG LO(I)     U         1.0            
 ZG LO(I)     X                        XCOEFF
 
 ND

CONSTANTS

 DO I         0                        M
 RI RI        I
 R* W         RI                       H
 R+ W         W                        LOWER
 
 RS 1-W       W         1.0
 R* W-W**2    W                        1-W
 
 Z  PT        LO(I)                    W-W**2
 ND

BOUNDS

 FR PT        'DEFAULT'

ENDATA