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GULF.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME GULF
* Problem :
* *********
* The Gulf RD test problem in 3 variables.
* This function is a nonlinear least squares with 99 groups. Each
* group has a nonlinear element of exponential type.
* The number of groups may be varied, but must be larger or equal to 3
* Source: problem 11 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#27
* SIF input: Ph. Toint, Dec 1989.
* classification SUR2-MN-3-0
* Number of groups
IE M 99
* Useful parameters
IE 1 1
VARIABLES
X1
X2
X3
GROUPS
DO I 1 M
XN G(I)
ND
CONSTANTS
DO I 1 M
RI RI I
RM TI RI 0.01
Z GULF G(I) TI
ND
BOUNDS
FR GULF 'DEFAULT'
START POINT
GULF X1 5.0
GULF X2 2.5
GULF X3 0.15
ELEMENT TYPE
EV GLF V1 V2
EV GLF V3
EP GLF T
ELEMENT USES
XT 'DEFAULT' GLF
DO I 1 M
RI RI I
RM TI RI 0.01
ZV E(I) V1 X1
ZV E(I) V2 X2
ZV E(I) V3 X3
ZP E(I) T TI
ND
GROUP TYPE
GV L2 GVAR
GROUP USES
XT 'DEFAULT' L2
DO I 1 M
XE G(I) E(I)
ND
OBJECT BOUND
LO GULF 0.0
* Solution
*LO SOLTN 0.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS GULF
TEMPORARIES
R V1SQ
R YMV2
R YMV2SQ
R LNYMV2
R A
R ALN
R AM1
R EXPMA
R AEXPMA
M LOG
M EXP
M ABS
INDIVIDUALS
* Gulfian function
T GLF
A V1SQ V1 * V1
A YMV2 25.0 + ( -50.0 * LOG( T ) )**(2.0/3.0)
A+ - V2
A AM1 A - 1.0
A YMV2SQ YMV2 * YMV2
A LNYMV2 LOG( ABS( YMV2 ) )
A A ABS( YMV2 )**V3 / V1
A ALN A * LNYMV2
A EXPMA EXP( - A )
A AEXPMA A * EXPMA
F EXPMA
G V1 AEXPMA / V1
G V2 V3 * AEXPMA / YMV2
G V3 - AEXPMA * LNYMV2
H V1 V1 ( A - 2.0 ) * AEXPMA / V1SQ
H V1 V2 V3 * AM1 * AEXPMA / ( V1 * YMV2 )
H V1 V3 - ALN * AEXPMA / V1
H V2 V2 V3 * AEXPMA * (1.0 + V3 * AM1 ) / YMV2SQ
H V2 V3 AEXPMA * ( 1.0 + V3 * ALN ) / YMV2
H V3 V3 ALN * LNYMV2 * EXPMA * AM1
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS GULF
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA