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PENALTY2.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME PENALTY2
* Problem :
* --------
* The second penalty function
* This is a nonlinear least-squares problem with M=2*N groups.
* Group 1 is linear.
* Groups 2 to N use 2 nonlinear elements.
* Groups N+1 to M-1 use 1 nonlinear element.
* Group M uses N nonlinear elements.
* The Hessian matrix is dense.
* Source: Problem 24 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#112 (p. 80)
* SIF input: Ph. Toint, Dec 1989.
* classification SUR2-AN-V-0
* Number of variables
*IE N 4 $-PARAMETER original value
*IE N 10 $-PARAMETER
*IE N 50 $-PARAMETER
*IE N 100 $-PARAMETER
IE N 200 $-PARAMETER
*IE N 500 $-PARAMETER
*IE N 1000 $-PARAMETER
* Problem parameters (see Buckley)
RE A 0.00001
RE B 1.0
* Other parameter definitions
IE 1 1
IE 2 2
IA N+1 N 1
I+ M N N
IA M-1 M -1
RF EM1/10 EXP -0.1
RD 1/A A 1.0
RD 1/B B 1.0
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
XN G(1) X(1) 1.0
ZN G(1) 'SCALE' 1/B
DO I 2 M-1
ZN G(I) 'SCALE' 1/A
ND
ZN G(M) 'SCALE' 1/B
CONSTANTS
PENALTY2 G1 0.2
DO I 2 N
IA I-1 I -1
RI RI I
RI RI-1 I-1
RM I/10 RI 0.1
RM I-1/10 RI-1 0.1
R( EI/10 EXP I/10
R( EI-1/10 EXP I-1/10
R+ YI EI/10 EI-1/10
Z PENALTY2 G(I) YI
ND
DO I N+1 M-1
Z PENALTY2 G(I) EM1/10
ND
X PENALTY2 G(M) 1.0
BOUNDS
FR PENALTY2 'DEFAULT'
START POINT
* Standard starting point (0.5, ..., 0.5 )
XV PENALTY2 'DEFAULT' 0.5
ELEMENT TYPE
EV E10 V
EV SQ V
ELEMENT USES
DO I 2 N
IA I-1 I -1
XT A(I) E10
ZV A(I) V X(I)
XT B(I) E10
ZV B(I) V X(I-1)
ND
DO I N+1 M-1
IM -N N -1
I+ I-N I -N
IA I-N+1 I-N 1
XT C(I) E10
ZV C(I) V X(I-N+1)
ND
DO J 1 N
XT D(J) SQ
ZV D(J) V X(J)
ND
GROUP TYPE
GV L2 GVAR
GROUP USES
XT G(1) L2
DO I 2 N
XT G(I) L2
XE G(I) A(I) B(I)
ND
DO I N+1 M-1
XT G(I) L2
XE G(I) C(I)
ND
XT G(M) L2
DO J 1 N
IM -J J -1
I+ N-J N -J
IA N-J+1 N-J 1
RI WI N-J+1
ZE G(M) D(J) WI
ND
OBJECT BOUND
* Least square problems are bounded below by zero
LO PENALTY2 0.0
* Solution
*LO SOLTN(4) 9.37629D-6
*LO SOLTN(10) 2.93660D-4
*LO SOLTN(50) 4.29609813
*LO SOLTN(100) 97096.0840
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS PENALTY2
TEMPORARIES
R EXPA
M EXP
R TWOW
INDIVIDUALS
* Exponential type
T E10
A EXPA EXP( 0.1 * V )
F EXPA
G V 0.1 * EXPA
H V V 0.01 * EXPA
* Square type
T SQ
F V * V
G V V + V
H V V 2.0
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS PENALTY2
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA