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MODBEALE.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME MODBEALE
* Problem :
* *********
* A variation on Beale's problem in 2 variables
* Source: An adaptation by Ph. Toint of Problem 5 in
* J.J. More', B.S. Garbow and K.E. Hillstrom,
* "Testing Unconstrained Optimization Software",
* ACM Transactions on Mathematical Software, vol. 7(1), pp. 17-41, 1981.
* See also Buckley#89.
* SIF input: Ph. Toint, Mar 2003.
* classification SUR2-AN-V-0
* The number of variables is 2 * N/2
*IE N/2 1 $-PARAMETER original value
*IE N/2 2 $-PARAMETER
*IE N/2 5 $-PARAMETER
*IE N/2 100 $-PARAMETER
*IE N/2 1000 $-PARAMETER
IE N/2 10000 $-PARAMETER
RE ALPHA 50.0 $-PARAMETER
* Define useful parameters
IE 1 1
I+ N N/2 N/2
IA N/2-1 N/2 -1
RD ALPHINV ALPHA 1.0
VARIABLES
DO J 1 N
X X(J)
ND
GROUPS
DO I 1 N/2-1
IA I-1 I -1
I+ 2I-1 I-1 I-1
IA J 2I-1 1
IA J+1 J 1
IA J+2 J 2
XN BA(I)
XN BB(I)
XN BC(I)
XN L(I) X(J+1) 6.0 X(J+2) -1.0
ZN L(I) 'SCALE' ALPHINV
ND
XN BA(N/2)
XN BB(N/2)
XN BC(N/2)
CONSTANTS
DO I 1 N/2
X MODBEALE BA(I) 1.5
X MODBEALE BB(I) 2.25
X MODBEALE BC(I) 2.625
ND
BOUNDS
FR MODBEALE 'DEFAULT'
START POINT
XV MODBEALE 'DEFAULT' 1.0
ELEMENT TYPE
EV PRODB V1 V2
EP PRODB POW
ELEMENT USES
T 'DEFAULT' PRODB
DO I 1 N/2
IA I-1 I -1
I+ 2I-1 I-1 I-1
IA J 2I-1 1
IA J+1 J 1
ZV AE(I) V1 X(J)
ZV AE(I) V2 X(J+1)
XP AE(I) POW 1.0
ZV BE(I) V1 X(J)
ZV BE(I) V2 X(J+1)
XP BE(I) POW 2.0
ZV CE(I) V1 X(J)
ZV CE(I) V2 X(J+1)
XP CE(I) POW 3.0
ND
GROUP TYPE
GV L2 GVAR
GROUP USES
T 'DEFAULT' L2
DO I 1 N/2
XE BA(I) AE(I)
XE BB(I) BE(I)
XE BC(I) CE(I)
ND
OBJECT BOUND
LO BEALE 0.0
* Solution
*LO SOLTN 0.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS MODBEALE
TEMPORARIES
R T
R POWM1
R W
INDIVIDUALS
* Product type elements
T PRODB
A T 1.0 - V2**POW
A POWM1 POW - 1.0
A W - POW * V2**POWM1
F V1 * T
G V1 T
G V2 V1 * W
H V1 V1 0.0
H V1 V2 W
H V2 V2 -V1 * POW * POWM1 * V2**(POW - 2.0)
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS MODBEALE
INDIVIDUALS
* Least-square groups
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA