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HALDMADS.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME HALDMADS
* Problem :
* *********
* A nonlinear minmax problem in five variables.
* Source:
* J. Hald and K. Madsen,
* "Combined LP and quasi-Newton methods for minimax optimization",
* Mathematical Programming 20, pp. 49-62, 1981.
* SIF input: Ph. Toint, Nov 1993.
* classification LOR2-AN-6-42
IE 1 1
IE 5 5
IE 21 21
RE T -1.0
DO I 1 21
A= Y(I) T
A( EY(I) EXP T
RA T T 0.1
OD I
VARIABLES
DO I 1 5
X X(I)
OD I
U
GROUPS
XN OBJ U 1.0
DO I 1 21
XL F(I) U -1.0
XL MF(I) U -1.0
OD I
CONSTANTS
DO I 1 21
Z HALDMADS F(I) EY(I)
AM -EY(I) EY(I) -1.0
Z HALDMADS MF(I) -EY(I)
OD I
BOUNDS
* All variables are free
FR HALDMADS 'DEFAULT'
START POINT
HALDMADS X1 0.5
ELEMENT TYPE
EV HM V1 V2
EV HM V3 V4
EV HM V5
EP HM Y
ELEMENT USES
DO I 1 21
XT EL(I) HM
ZV EL(I) V1 X1
ZV EL(I) V2 X2
ZV EL(I) V3 X3
ZV EL(I) V4 X4
ZV EL(I) V5 X5
ZP EL(I) Y Y(I)
OD I
GROUP USES
DO I 1 21
XE F(I) EL(I) 1.0
XE MF(I) EL(I) -1.0
OD I
OBJECT BOUND
* Solution
*LO SOLTN 0.0001207
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS HALDMADS
TEMPORARIES
R N
R D
R YY
R YYY
R DD
R DDD
INDIVIDUALS
T HM
A YY Y * Y
A YYY YY * Y
A N V1 + Y * V2
A D 1.0 + V3 * Y + V4 * YY + V5 * YYY
A DD D * D
A DDD DD * D
F N / D
G V1 1.0 / D
G V2 Y / D
G V3 - N * Y / DD
G V4 - N * YY / DD
G V5 - N * YYY / DD
H V1 V3 - Y / DD
H V1 V4 - YY / DD
H V1 V5 - YYY / DD
H V2 V3 - YY / DD
H V2 V4 - YYY / DD
H V2 V5 - YY * YY / DD
H V3 V3 2.0 * N * YY / DDD
H V3 V4 2.0 * N * YYY / DDD
H V3 V5 2.0 * N * YY * YY / DDD
H V4 V4 2.0 * N * YY * YY / DDD
H V4 V5 2.0 * N * YY * YYY / DDD
H V5 V5 2.0 * N * YYY * YYY / DDD
ENDATA