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BROWNDEN.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME BROWNDEN
* Problem :
* *********
* Brown and Dennis problem in 4 variables.
* This function is a nonlinear least squares with 20 groups. Each
* group has 2 nonlinear elements.
* Source: Problem 16 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#30
* SIF input: Ph. Toint, Dec 1989.
* classification SUR2-AN-4-0
* Number of groups
IE M 20
* Useful parameters
IE 1 1
VARIABLES
X1
X2
X3
X4
GROUPS
DO I 1 M
XN G(I)
ND
BOUNDS
FR BROWNDEN 'DEFAULT'
START POINT
BROWNDEN X1 25.0
BROWNDEN X2 5.0
BROWNDEN X3 -5.0
BROWNDEN X4 -1.0
ELEMENT TYPE
EV BRD V1 V2
EP BRD CV2 CIND
ELEMENT USES
XT 'DEFAULT' BRD
DO I 1 M
RI RI I
RM I/5 RI 0.2
R( EI5 EXP I/5
ZV A(I) V1 X1
ZV A(I) V2 X2
ZP A(I) CV2 I/5
ZP A(I) CIND EI5
R( SI5 SIN I/5
R( CI5 COS I/5
ZV B(I) V1 X3
ZV B(I) V2 X4
ZP B(I) CV2 SI5
ZP B(I) CIND CI5
ND
GROUP TYPE
GV L2 GVAR
GROUP USES
XT 'DEFAULT' L2
DO I 1 M
XE G(I) A(I) B(I)
ND
OBJECT BOUND
LO BROWNDEN 0.0
* Solution
*LO SOLTN 85822.2
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS BROWNDEN
TEMPORARIES
R A
M EXP
M SIN
M COS
INDIVIDUALS
* Square of a linear combination
T BRD
A A V1 + CV2 * V2 - CIND
F A * A
G V1 2.0 * A
G V2 2.0 * A * CV2
H V1 V1 2.0
H V1 V2 2.0 * CV2
H V2 V2 2.0 * CV2 * CV2
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS BROWNDEN
INDIVIDUALS
* Least-square groups
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA