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OET5.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME OET5
* 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 = [0.25,1]
* phi(x,w) = sqrt(w) - x4 - (x1 w^2 + x2 w + x3 )^2
* 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 LQR2-AN-5-V
* Discretization
*IE M 2
*IE M 100
IE M 500
* Define the interval
RE LOWER 0.25
RE UPPER 1.0
* Define constants
IE 0 0
IE 1 1
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 X4 -1.0
XG UP(I) U 1.0 X4 1.0
ND
CONSTANTS
DO I 0 M
RI RI I
R* W RI H
R+ W W LOWER
R( SQRTW SQRT W
RM -SQRTW SQRTW -1.0
Z OET5 LO(I) -SQRTW
Z OET5 UP(I) SQRTW
ND
BOUNDS
FR OET5 'DEFAULT'
START POINT
V OET5 'DEFAULT' 1.0
ELEMENT TYPE
EV QUAD X1 X2
EV QUAD X3
EP QUAD W
ELEMENT USES
DO I 0 M
RI RI I
R* W RI H
R+ W W LOWER
XT E(1,I) QUAD
ZV E(1,I) X1 X1
ZV E(1,I) X2 X2
ZV E(1,I) X3 X3
ZP E(1,I) W W
ND
GROUP USES
DO I 0 M
XE LO(I) E(1,I)
XE UP(I) E(1,I) -1.0
ND
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS OET5
TEMPORARIES
R W2
R TERM
INDIVIDUALS
T QUAD
A W2 W * W
A TERM W2 * X1 + W * X2 + X3
F TERM * TERM
G X1 2.0 * TERM * W2
G X2 2.0 * TERM * W
G X3 2.0 * TERM
H X1 X1 2.0 * W2 * W2
H X2 X1 2.0 * W2 * W
H X3 X1 2.0 * W2
H X2 X2 2.0 * W2
H X3 X2 2.0 * W
H X3 X3 2.0
ENDATA