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HIMMELBF.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME HIMMELBF
* Problem :
* *********
* A 4 variables data fitting problems by Himmelblau.
* Source: problem 32 in
* D.H. Himmelblau,
* "Applied nonlinear programming",
* McGraw-Hill, New-York, 1972.
* See Buckley#76 (p. 66)
* SIF input: Ph. Toint, Dec 1989.
* classification SUR2-AN-4-0
* Problem data
RE A1 0.0
RE A2 0.000428
RE A3 0.001000
RE A4 0.001610
RE A5 0.002090
RE A6 0.003480
RE A7 0.005250
RE B1 7.391
RE B2 11.18
RE B3 16.44
RE B4 16.20
RE B5 22.20
RE B6 24.02
RE B7 31.32
* Parameters
IE 1 1
IE 7 7
VARIABLES
X1
X2
X3
X4
GROUPS
DO I 1 7
XN G(I) 'SCALE' 0.0001
ND
CONSTANTS
X HIMMELBF 'DEFAULT' 1.0
BOUNDS
FR HIMMELBF 'DEFAULT'
START POINT
HIMMELBF X1 2.7
HIMMELBF X2 90.0
HIMMELBF X3 1500.0
HIMMELBF X4 10.0
ELEMENT TYPE
EV HF XA XB
EV HF XC XD
EP HF A B
ELEMENT USES
T 'DEFAULT' HF
DO I 1 7
ZV E(I) XA X1
ZV E(I) XB X2
ZV E(I) XC X3
ZV E(I) XD X4
ZP E(I) A A(I)
ZP E(I) B B(I)
ND
GROUP TYPE
GV L2 GVAR
GROUP USES
T 'DEFAULT' L2
DO I 1 7
XE G(I) E(I)
ND
OBJECT BOUND
* Solution
*LO SOLTN 318.572
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS HIMMELBF
TEMPORARIES
R U
R V
R V2
R AB
R A2
R T
INDIVIDUALS
T HF
A U XA * XA + A * XB * XB + A * A * XC * XC
A V B * ( 1.0 + A * XD * XD )
A V2 V * V
A AB A * B
A A2 A * A
A T -4.0 * AB / V2
F U / V
G XA 2.0 * XA / V
G XB 2.0 * A * XB / V
G XC 2.0 * A2* XC / V
G XD - 2.0 * AB * XD * U / V2
H XA XA 2.0 / V
H XA XD T * XD * XA
H XB XB 2.0 * A / V
H XB XD T * A * XD * XB
H XC XC 2.0 * A2 / V
H XC XD T * A * XD * XC
H XD XD -2.0 * AB * U / V2
H+ + 8.0 * ( AB * XD ) **2 * U / ( V2 * V )
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS HIMMELBF
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA