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HELIX.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME HELIX
* Problem :
* *********
* The "Helix" problem in 3 variables
* Source: problem 7 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#12 (p. 58)
* SIF input: Ph. Toint, Dec 1989.
* classification SUR2-AN-3-0
* Define useful parameters
IE 1 1
VARIABLES
X1
X2
X3
GROUPS
N A X3 1.0
N A 'SCALE' 0.01
N B 'SCALE' 0.01
N C X3 1.0
CONSTANTS
HELIX B 1.0
BOUNDS
* All variables are free
FR HELIX 'DEFAULT'
START POINT
XV HELIX 'DEFAULT' 0.0
HELIX X1 -1.0
ELEMENT TYPE
EV THETA V1 V2
EV TWONRM V1 V2
ELEMENT USES
T AE THETA
V AE V1 X1
V AE V2 X2
T BE TWONRM
V BE V1 X1
V BE V2 X2
GROUP TYPE
GV L2 GVAR
GROUP USES
XT 'DEFAULT' L2
E A AE -10.0
E B BE
OBJECT BOUND
LO HELIX 0.0
* Solution
*LO SOLTN 0.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS HELIX
TEMPORARIES
R TWOPII
R T2
R T4
R HD
R V1SQ
R V2SQ
R R2
R SQT
R R2SQT
R HUGE
M SQRT
M ATAN2
GLOBALS
A TWOPII 0.15915494
INDIVIDUALS
* Theta
T THETA
A V1SQ V1 * V1
A V2SQ V2 * V2
A R2 V1SQ + V2SQ
A T2 TWOPII / R2
A T4 T2 / R2
A HD 2.0 * T4 * V1 * V2
F TWOPII * ATAN2( V2, V1 )
G V1 - T2 * V2
G V2 T2 * V1
H V1 V1 HD
H V1 V2 T4 * ( V2SQ - V1SQ )
H V2 V2 - HD
* The 2-norm
T TWONRM
A V1SQ V1 * V1
A V2SQ V2 * V2
A R2 V1SQ + V2SQ
A SQT SQRT( R2 )
A R2SQT R2 * SQT
F SQT
G V1 V1 / SQT
G V2 V2 / SQT
H V1 V1 V2SQ / R2SQT
H V1 V2 - V1 * V2 / R2SQT
H V2 V2 V1SQ / R2SQT
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS HELIX
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA