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HET-Z.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME HET-Z
* 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 = [-1,1]
* phi(x,w) = (1-w^2) - (0.5 x^2 - 2 x w )
* Source: R. Hettich and P. Znecke,
* "Numerische Methoden der Approximation und semi-infiniter optimierung",
* Teubener Studienbucher, 1982
* SIF input: Nick Gould, February, 1994.
* classification LQR2-AN-2-V
* Discretization
*IE M 2
*IE M 100
IE M 500
* Define the interval
RE LOWER -1.0
RE UPPER 1.0
* Define constants
RE ONE 1.0
IE 0 0
IE 1 1
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
RM 2W W 2.0
RM -2W 2W -1.0
XG LO(I) U 1.0
ZG LO(I) X 2W
XG UP(I) U 1.0
ZG UP(I) X -2W
ND
CONSTANTS
DO I 0 M
RI RI I
R* W RI H
R+ W W LOWER
R* W**2 W W
RS 1-W**2 W**2 1.0
RM -1+W**2 1-W**2 -1.0
Z HET-Z LO(I) -1+W**2
Z HET-Z UP(I) 1-W**2
ND
BOUNDS
FR HET-Z 'DEFAULT'
ELEMENT TYPE
EV QUAD X
ELEMENT USES
T QUAD QUAD
V QUAD X X
GROUP USES
DO I 0 M
XE LO(I) QUAD -1.0
XE UP(I) QUAD
ND
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS HET-Z
INDIVIDUALS
T QUAD
F 0.5 * X * X
G X X
H X X 1.0
ENDATA