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PENALTY3.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME PENALTY3
* Problem :
* *********
* A penalty problem by Gill, Murray and Pitfield.
* It has a dense Hessian matrix.
* Source: problem 114 (p. 81) in
* A.R. Buckley,
* "Test functions for unconstrained minimization",
* TR 1989CS-3, Mathematics, statistics and computing centre,
* Dalhousie University, Halifax (CDN), 1989.
* SIF input: Nick Gould, Dec 1990.
* classification OUR2-AY-V-0
* N is the number of variables
*IE N/2 25 $-PARAMETER n = 50 original value
*IE N/2 50 $-PARAMETER n = 100
IE N/2 100 $-PARAMETER n = 200
* Obtain N from N/2
IM N N/2 2
* Define useful parameters
IE 1 1
IE 2 2
IA N-2 N -2
IA N-1 N -1
IA N-2 N -2
RI RN N
RE A 0.001
RM MINUSA A -1.0
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
N A
N REXP
N SEXP
N RS
N T**2
N U
CONSTANTS
Z PENALTY3 A MINUSA
BOUNDS
FR PENALTY3 'DEFAULT'
START POINT
* Starting from ( 1, -1, 1, -1, ...., 1, -1 )
DO I 1 N
DI I 2
IA IP1 I 1
X PENALTY3 X(I) 1.0
X PENALTY3 X(IP1) -1.0
ND
ELEMENT TYPE
* REXP = A*(U1 - 1)**2 * EXP( U3 ), where
* U1 = XI + 2 XIP1 + 10 XIP2 and U3 = XN
EV REXP XI XIP1
EV REXP XIP2 XN
IV REXP U1 U3
EP REXP A
* SEXP = A*(U2 - 3)**2 * EXP( U3 ), where
* U2 = 2 XJ + XJP1 and U3 = XNM1
EV SEXP XJ XJP1
EV SEXP XNM1
IV SEXP U2 U3
EP SEXP A
* RS = A*(U1 - 1)**2 * (U2 - 3)**2, where
* U1 = XI + 2 XIP1 + 10 XIP2 and U2 = 2 XJ + XJP1
EV RS XI XIP1
EV RS XIP2 XJ
EV RS XJP1
IV RS U1 U2
EP RS A
* T = (XI**2 - RN) * (XJ**2 - RN)
EV T XI XJ
EP T RN
* U = (XI - 1)**2
EV U XI
ELEMENT USES
DO I 1 N-2
IA I+1 I 1
IA I+2 I 2
XT REXP(I) REXP
ZV REXP(I) XI X(I)
ZV REXP(I) XIP1 X(I+1)
ZV REXP(I) XIP2 X(I+2)
ZV REXP(I) XN X(N)
ZP REXP(I) A A
ND
DO J 1 N-2
IA J+1 J 1
XT SEXP(J) SEXP
ZV SEXP(J) XJ X(J)
ZV SEXP(J) XJP1 X(J+1)
ZV SEXP(J) XNM1 X(N-1)
ZP SEXP(J) A A
ND
DO I 1 N-2
IA I+1 I 1
IA I+2 I 2
DO J 1 N-2
IA J+1 J 1
XT RS(I,J) RS
ZV RS(I,J) XI X(I)
ZV RS(I,J) XIP1 X(I+1)
ZV RS(I,J) XIP2 X(I+2)
ZV RS(I,J) XJ X(J)
ZV RS(I,J) XJP1 X(J+1)
ZP RS(I,J) A A
ND
DO I 1 N
DO J 1 N
XT T(I,J) T
ZV T(I,J) XI X(I)
ZV T(I,J) XJ X(J)
ZP T(I,J) RN RN
ND
DO I 1 N/2
XT U(I) U
ZV U(I) XI X(I)
ND
GROUP USES
DO I 1 N-2
XE REXP REXP(I)
XE SEXP SEXP(I)
DO J 1 N-2
XE RS RS(I,J)
ND
DO I 1 N
DO J 1 N
XE T**2 T(I,J)
ND
DO I 1 N/2
XE U U(I)
ND
OBJECT BOUND
LO PENALTY3 0.0
* Solution
*LO SOLTN 0.001
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS PENALTY3
TEMPORARIES
R U1M1
R EXPU3
M EXP
R F
R GU1
R U2M3
R GU2
R XI2MRN
R XJ2MRN
R XIM1
INDIVIDUALS
* REXP elements
T REXP
R U1 XI 1.0 XIP1 2.0
R U1 XIP2 10.0
R U3 XN 1.0
A U1M1 U1 - 1.0D+0
A EXPU3 EXP( U3 )
A F A * U1M1 * U1M1 * EXPU3
A GU1 2.0D+0 * A * U1M1 * EXPU3
F F
G U1 GU1
G U3 F
H U1 U1 2.0D+0 * A * EXPU3
H U1 U3 GU1
H U3 U3 F
* SEXP elements
T SEXP
R U2 XJ 2.0 XJP1 1.0
R U3 XNM1 1.0
A U2M3 U2 - 3.0D+0
A EXPU3 EXP( U3 )
A F A * U2M3 * U2M3 * EXPU3
A GU2 2.0D+0 * A * U2M3 * EXPU3
F F
G U2 GU2
G U3 F
H U2 U2 2.0D+0 * A * EXPU3
H U2 U3 GU2
H U3 U3 F
* RS element
T RS
R U1 XI 1.0 XIP1 2.0
R U1 XIP2 10.0
R U2 XJ 2.0 XJP1 1.0
A U1M1 U1 - 1.0D+0
A U2M3 U2 - 3.0D+0
F A * U2M3 * U2M3 * U1M1 * U1M1
G U1 2.0D+0 * A * U2M3 * U2M3 * U1M1
G U2 2.0D+0 * A * U1M1 * U1M1 * U2M3
H U1 U1 2.0D+0 * A * U2M3 * U2M3
H U1 U2 4.0D+0 * A * U1M1 * U2M3
H U2 U2 2.0D+0 * A * U1M1 * U1M1
* T element
T T
A XI2MRN XI*XI - RN
A XJ2MRN XJ*XJ - RN
F XI2MRN * XJ2MRN
G XI 2.0D+0 * XI * XJ2MRN
G XJ 2.0D+0 * XJ * XI2MRN
H XI XI 2.0D+0 * XJ2MRN
H XI XJ 4.0D+0 * XI * XJ
H XJ XJ 2.0D+0 * XI2MRN
* U element
T U
A XIM1 XI - 1.0D+0
F XIM1 * XIM1
G XI XIM1 + XIM1
H XI XI 2.0D+0
ENDATA