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CHAINWOO.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME CHAINWOO
* Problem :
* *********
* The chained Woods problem, a variant on Woods function
* This problem is a sum of n/2 sets of 6 terms, each of which is
* assigned its own group. For a given set i, the groups are
* A(i), B(i), C(i), D(i), E(i) and F(i). Groups A(i) and C(i) contain 1
* nonlinear element each, denoted Y(i) and Z(i).
* The problem dimension is defined from the number of these sets.
* The number of problem variables is then 2 times + 2 as large
* This version uses a slightly unorthodox expression of Woods
* function as a sum of squares (see Buckley)
* Source: problem 8 in
* A.R.Conn,N.I.M.Gould and Ph.L.Toint,
* "Testing a class of methods for solving minimization
* problems with simple bounds on their variables,
* Mathematics of Computation 50, pp 399-430, 1988.
* SIF input: Nick Gould and Ph. Toint, Dec 1995.
* classification SUR2-AN-V-0
* NS is the number of sets (= (n-2)/2)
*IE NS 1 $-PARAMETER n= 4
*IE NS 49 $-PARAMETER n = 100
*IE NS 499 $-PARAMETER n = 1000 original value
IE NS 1999 $-PARAMETER n = 4000
*IE NS 4999 $-PARAMETER n = 10000
* Problem dimension
IM N NS 2
IA N N 2
* Define useful parameters
IE 1 1
IE 2 2
RE 1.0 1.0
RE 90.0 90.0
R/ 1/90 1.0 90.0
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
N CONST
IE J 4
DO I 1 NS
IA J-1 J -1
IA J-2 J -2
IA J-3 J -3
XN A(I) X(J-2) 1.0
XN A(I) 'SCALE' 0.01
XN B(I) X(J-3) -1.0
XN C(I) X(J) 1.0
ZN C(I) 'SCALE' 1/90
XN D(I) X(J-1) -1.0
XN E(I) X(J-2) 1.0 X(J) 1.0
XN E(I) 'SCALE' 0.1
XN F(I) X(J-2) 1.0 X(J) -1.0
XN F(I) 'SCALE' 10.0
IA J J 2
ND
CONSTANTS
X CHAINWOO CONST 1.0
DO I 1 NS
X CHAINWOO B(I) -1.0
X CHAINWOO D(I) -1.0
X CHAINWOO E(I) 2.0
ND
BOUNDS
FR CHAINWOO 'DEFAULT'
START POINT
X CHAINWOO 'DEFAULT' -2.0
X CHAINWOO X1 -3.0
X CHAINWOO X2 -1.0
X CHAINWOO X3 -3.0
X CHAINWOO X4 -1.0
ELEMENT TYPE
EV MSQ V
ELEMENT USES
IE J 4
DO I 1 NS
IA J-1 J -1
IA J-3 J -3
XT Y(I) MSQ
ZV Y(I) V X(J-3)
XT Z(I) MSQ
ZV Z(I) V X(J-1)
IA J J 2
ND
GROUP TYPE
GV L2 GVAR
GROUP USES
T 'DEFAULT' L2
DO I 1 NS
XE A(I) Y(I)
XE C(I) Z(I)
ND
OBJECT BOUND
* Least square problems are bounded below by zero
LO CHAINWOO 0.0
* Solution
*LO SOLTN 0.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS CHAINWOO
INDIVIDUALS
* Minus square elements
T MSQ
F - V * V
G V - V - V
H V V - 2.0
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS CHAINWOO
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA