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DIXCHLNV.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME DIXCHLNV
* Problem :
* *********
* A variant of a constrained problem set as a challenge for SQP methods
* by L.C.W. Dixon at the APMOD91 Conference.
* The variant from the original problem is that the variables have
* been constrained to be above 1.0D-15, which in turn allows the
* constraints to be expressed in terms of logarithms.
* Source: a modification (by Ph. Toint) of
* L.C.W. Dixon, personnal communication, Jan 1991.
* SIF input: Ph. Toint, Feb 1991.
* classification SOR2-AN-V-V
* Number of variables
* (variable, but must be even and at least equal to 4)
*IE N 10 $-PARAMETER
*IE N 50 $-PARAMETER
*IE N 100 $-PARAMETER original value
IE N 1000 $-PARAMETER
*IE N 5000 $-PARAMETER
* Other parameters
IE 1 1
IE 2 2
IA N-3 N -3
IA N-1 N -1
RE 90.0 90.0
RE 10.1 10.1
RE 19.8 19.8
RD 1/90.0 90.0 1.0
RD 1/10.1 10.1 1.0
RD 1/19.8 19.8 1.0
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
* Objective groups
DO I 1 N-3
IA I+1 I 1
IA I+2 I 2
IA I+3 I 3
XN A(I) X(I+1) 1.0
XN A(I) 'SCALE' 0.01
XN B(I) X(I) 1.0
XN C(I) X(I+3) 1.0
ZN C(I) 'SCALE' 1/90.0
XN D(I) X(I+2) 1.0
XN E(I) X(I+1) 1.0
ZN E(I) 'SCALE' 1/10.1
XN F(I) X(I+3) 1.0
ZN F(I) 'SCALE' 1/10.1
XN G(I)
ZN G(I) 'SCALE' 1/19.8
OD I
* Constraints
DO I 2 N
DI I 2
XE P(I)
OD I
CONSTANTS
DO I 1 N-3
X DIXCHLNV B(I) 1.0
X DIXCHLNV D(I) 1.0
X DIXCHLNV E(I) 1.0
X DIXCHLNV F(I) 1.0
OD I
BOUNDS
LO DIXCHLNV 'DEFAULT' 1.0D-8
START POINT
RE X0 2.0
DO I 1 N-1
DI I 2
ZV DIXCHLNV X(I) X0
RD 1/X0 X0 1.0
IA I+1 I 1
ZV DIXCHLNV X(I+1) 1/X0
RA X0 X0 1.0
OD I
ELEMENT TYPE
EV SQ V
EV S2PR V W
EV LOGV V
ELEMENT USES
DO I 1 N-1
XT XSQ(I) SQ
ZV XSQ(I) V X(I)
OD I
DO I 1 N-3
IA I+1 I 1
IA I+3 I 3
XT PR(I) S2PR
ZV PR(I) V X(I+1)
ZV PR(I) W X(I+3)
OD I
DO I 1 N
XT LOGX(I) LOGV
ZV LOGX(I) V X(I)
OD I
GROUP TYPE
GV L2 GVAR
GROUP USES
* Objective groups
DO I 1 N-3
IA I+2 I 2
XT A(I) L2
XE A(I) XSQ(I) -1.0
XT B(I) L2
XT C(I) L2
XE C(I) XSQ(I+2) -1.0
XT D(I) L2
XT E(I) L2
XT F(I) L2
XE G(I) PR(I)
OD I
* Constraints
DO I 2 N
DI I 2
DO J 1 I
XE P(I) LOGX(J)
OD J
OD I
OBJECT BOUND
* Solution
*LO SOLTN 0.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS DIXCHLNV
TEMPORARIES
M LOG
INDIVIDUALS
T SQ
F V * V
G V V + V
H V V 2.0
T LOGV
F LOG(V)
G V 1.0 / V
H V V -1.0 / ( V * V )
T S2PR
F ( V - 1.0 ) * ( W - 1.0 )
G V W - 1.0
G W V - 1.0
H V W 1.0
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS DIXCHLNV
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA