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BARD.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME BARD
* Problem :
* *********
* Bard problem in 3 variables.
* This function is a nonlinear least squares with 15 groups. Each
* group has a linear and a nonlinear element.
* Source: Problem 3 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#16.
* SIF input: Ph. Toint, Dec 1989.
* classification SUR2-AN-3-0
* Number of groups
IE 15 15
* Useful parameters
IE 1 1
IE 8 8
IE 9 9
VARIABLES
X1
X2
X3
GROUPS
DO I 1 15
XN G(I) X1 1.0
ND
CONSTANTS
BARD G1 0.14
BARD G2 0.18
BARD G3 0.22
BARD G4 0.25
BARD G5 0.29
BARD G6 0.32
BARD G7 0.35
BARD G8 0.39
BARD G9 0.37
BARD G10 0.58
BARD G11 0.73
BARD G12 0.96
BARD G13 1.34
BARD G14 2.10
BARD G15 4.39
BOUNDS
FR BARD 'DEFAULT'
START POINT
XV BARD 'DEFAULT' 1.0
ELEMENT TYPE
EV BD V1 V2
EP BD U V
EP BD W
ELEMENT USES
T 'DEFAULT' BD
DO I 1 8
RI REALI I
RS 16-I REALI 16.0
ZV E(I) V1 X2
ZV E(I) V2 X3
ZP E(I) U REALI
ZP E(I) V 16-I
ZP E(I) W REALI
ND
DO I 9 15
RI REALI I
RS 16-I REALI 16.0
ZV E(I) V1 X2
ZV E(I) V2 X3
ZP E(I) U REALI
ZP E(I) V 16-I
ZP E(I) W 16-I
ND
GROUP TYPE
GV L2 GVAR
GROUP USES
T 'DEFAULT' L2
DO I 1 15
XE G(I) E(I)
ND
OBJECT BOUND
LO BARD 0.0
* Solution
* LO SOLTN 8.2149D-03
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS BARD
TEMPORARIES
R Z
R Z2
R Z3
R VU
R WU
INDIVIDUALS
* Bard function
T BD
A Z V * V1 + W * V2
A Z2 Z * Z
A Z3 Z * Z2
A VU V * U
A WU W * U
F U / Z
G V1 - VU / Z2
G V2 - WU / Z2
H V1 V1 2.0 * V * VU / Z3
H V1 V2 2.0 * V * WU / Z3
H V2 V2 2.0 * W * WU / Z3
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS BARD
INDIVIDUALS
* Least-square groups
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA