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OSBORNEB.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME OSBORNEB
* Problem :
* *********
* Osborne second problem in 11 variables.
* This function is a nonlinear least squares with 65 groups. Each
* group has 4 nonlinear elements.
* Source: Problem 19 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#32 (p.78).
* SIF input: Ph. Toint, Dec 1989.
* classification SUR2-MN-11-0
* Number of groups
IE M 65
* Number of variables
IE N 11
* Useful parameters
IE 1 1
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
DO I 1 M
XN G(I)
ND
CONSTANTS
OSBORNEB G1 1.366
OSBORNEB G2 1.191
OSBORNEB G3 1.112
OSBORNEB G4 1.013
OSBORNEB G5 0.991
OSBORNEB G6 0.885
OSBORNEB G7 0.831
OSBORNEB G8 0.847
OSBORNEB G9 0.786
OSBORNEB G10 0.725
OSBORNEB G11 0.746
OSBORNEB G12 0.679
OSBORNEB G13 0.608
OSBORNEB G14 0.655
OSBORNEB G15 0.616
OSBORNEB G16 0.606
OSBORNEB G17 0.602
OSBORNEB G18 0.626
OSBORNEB G19 0.651
OSBORNEB G20 0.724
OSBORNEB G21 0.649
OSBORNEB G22 0.649
OSBORNEB G23 0.694
OSBORNEB G24 0.644
OSBORNEB G25 0.624
OSBORNEB G26 0.661
OSBORNEB G27 0.612
OSBORNEB G28 0.558
OSBORNEB G29 0.533
OSBORNEB G30 0.495
OSBORNEB G31 0.500
OSBORNEB G32 0.423
OSBORNEB G33 0.395
OSBORNEB G34 0.375
OSBORNEB G35 0.372
OSBORNEB G36 0.391
OSBORNEB G37 0.396
OSBORNEB G38 0.405
OSBORNEB G39 0.428
OSBORNEB G40 0.429
OSBORNEB G41 0.523
OSBORNEB G42 0.562
OSBORNEB G43 0.607
OSBORNEB G44 0.653
OSBORNEB G45 0.672
OSBORNEB G46 0.708
OSBORNEB G47 0.633
OSBORNEB G48 0.668
OSBORNEB G49 0.645
OSBORNEB G50 0.632
OSBORNEB G51 0.591
OSBORNEB G52 0.559
OSBORNEB G53 0.597
OSBORNEB G54 0.625
OSBORNEB G55 0.739
OSBORNEB G56 0.710
OSBORNEB G57 0.729
OSBORNEB G58 0.720
OSBORNEB G59 0.636
OSBORNEB G60 0.581
OSBORNEB G61 0.428
OSBORNEB G62 0.292
OSBORNEB G63 0.162
OSBORNEB G64 0.098
OSBORNEB G65 0.054
BOUNDS
FR OSBORNEB 'DEFAULT'
START POINT
* Standard starting point
OSBORNEB X1 1.3
OSBORNEB X2 0.65
OSBORNEB X3 0.65
OSBORNEB X4 0.7
OSBORNEB X5 0.6
OSBORNEB X6 3.0
OSBORNEB X7 5.0
OSBORNEB X8 7.0
OSBORNEB X9 2.0
OSBORNEB X10 4.5
OSBORNEB X11 5.5
ELEMENT TYPE
EV PEXP V1 V2
EP PEXP T
EV PEXP3 V1 V2
EV PEXP3 V3
EP PEXP3 T3
ELEMENT USES
DO I 1 M
IA I-1 I 1
RI RI-1 I-1
RM TI RI-1 0.1
XT A(I) PEXP
ZV A(I) V1 X1
ZV A(I) V2 X5
ZP A(I) T TI
XT B(I) PEXP3
ZV B(I) V1 X2
ZV B(I) V2 X9
ZV B(I) V3 X6
ZP B(I) T3 TI
XT C(I) PEXP3
ZV C(I) V1 X3
ZV C(I) V2 X10
ZV C(I) V3 X7
ZP C(I) T3 TI
XT D(I) PEXP3
ZV D(I) V1 X4
ZV D(I) V2 X11
ZV D(I) V3 X8
ZP D(I) T3 TI
ND
GROUP TYPE
GV L2 GVAR
GROUP USES
XT 'DEFAULT' L2
DO I 1 M
XE G(I) A(I) B(I)
XE G(I) C(I) D(I)
ND
OBJECT BOUND
* Least square problems are bounded below by zero
LO OSBORNEB 0.0
* Solution
*LO SOLTN 0.04013774
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS OSBORNEB
TEMPORARIES
R EXPA
R FVAL
R TMV2
R TMV2SQ
R A
M EXP
INDIVIDUALS
* Parametric product with exponential
T PEXP
A EXPA EXP( - T * V2 )
A FVAL V1 * EXPA
F FVAL
G V1 EXPA
G V2 - T * FVAL
H V1 V2 - T * EXPA
H V2 V2 T * T * FVAL
* Second type
T PEXP3
A TMV2 T3 - V2
A TMV2SQ TMV2 * TMV2
A EXPA EXP( - TMV2SQ * V3 )
A FVAL V1 * EXPA
A A 2.0 * TMV2 * V3
F FVAL
G V1 EXPA
G V2 A * FVAL
G V3 -TMV2SQ * FVAL
H V1 V2 A * EXPA
H V1 V3 -TMV2SQ * EXPA
H V2 V2 ( A * A - 2.0 * V3 ) * FVAL
H V2 V3 ( 2.0 * TMV2 - A * TMV2SQ ) * FVAL
H V3 V3 TMV2SQ * TMV2SQ * FVAL
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS OSBORNEB
INDIVIDUALS
* Least-square groups
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA