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PENALTY1.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME PENALTY1
* Problem :
* *********
* This problem is a sum of n+1 least-squares groups, the first n of
* which have only a linear element.
* It Hessian matrix is dense.
* Source: Problem 23 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 #181 (p. 79).
* SIF input: Ph. Toint, Dec 1989.
* classification SUR2-AN-V-0
* N is the number of free variables
*IE N 4 $-PARAMETER
*IE N 10 $-PARAMETER
*IE N 50 $-PARAMETER
*IE N 100 $-PARAMETER
*IE N 500 $-PARAMETER
IE N 1000 $-PARAMETER
IA M N 1
* Define useful parameters
IE 1 1
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
DO I 1 N
XN G(I) X(I) 1.0
XN G(I) 'SCALE' 100000.0
ND
XN G(M)
CONSTANTS
DO I 1 N
X PENALTY1 G(I) 1.0
ND
X PENALTY1 G(M) 0.25
BOUNDS
FR PENALTY1 'DEFAULT'
START POINT
DO I 1 N
RI REALI I
Z PENALTY1 X(I) REALI
ND
ELEMENT TYPE
EV SQ V1
ELEMENT USES
DO I 1 N
XT E(I) SQ
ZV E(I) V1 X(I)
ND
GROUP TYPE
GV L2 GVAR
GROUP USES
XT 'DEFAULT' L2
DO I 1 N
XE G(M) E(I)
ND
OBJECT BOUND
* Least square problems are bounded below by zero
LO PENALTY1 0.0
* Solution
*LO SOLTN(4) 2.24997D-4
*LO SOLTN(10) 7.08765D-5
*LO SOLTN(50) ???
*LO SOLTN(100) ???
*LO SOLTN(500) ???
*LO SOLTN(1000) ???
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS PENALTY1
INDIVIDUALS
* Square type elements
T SQ
F V1 * V1
G V1 V1 + V1
H V1 V1 2.0
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS PENALTY1
INDIVIDUALS
* Weighted least-square groups
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA