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BDQRTIC.SIF
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BDQRTIC.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME BDQRTIC
* Problem :
* *********
* This problem is quartic and has a banded Hessian with bandwidth = 9
* Source: Problem 61 in
* A.R. Conn, N.I.M. Gould, M. Lescrenier and Ph.L. Toint,
* "Performance of a multifrontal scheme for partially separable
* optimization",
* Report 88/4, Dept of Mathematics, FUNDP (Namur, B), 1988.
* SIF input: Ph. Toint, Dec 1989.
* classification SUR2-AN-V-0
* Number of variables (variable)
*IE N 100 $-PARAMETER original value
*IE N 500 $-PARAMETER
*IE N 1000 $-PARAMETER
IE N 5000 $-PARAMETER
* Number of groups
IA N-4 N -4
* Define useful parameters
IE 1 1
IE 2 2
IA N+1 N 1
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
DO I 1 N-4
XN L(I) X(I) -4.0
XN G(I)
ND
CONSTANTS
DO I 1 N-4
X BDQRTIC L(I) -3.0
ND
BOUNDS
FR BDQRTIC 'DEFAULT'
START POINT
X BDQRTIC 'DEFAULT' 1.0
ELEMENT TYPE
EV SQ EVAR
ELEMENT USES
T 'DEFAULT' SQ
DO I 1 N
ZV A(I) EVAR X(I)
ND
GROUP TYPE
GV L2 GVAR
GROUP USES
T 'DEFAULT' L2
DO I 1 N-4
IA I+1 I 1
IA I+2 I 2
IA I+3 I 3
XE G(I) A(I) 1.0 A(I+1) 2.0
XE G(I) A(I+2) 3.0 A(I+3) 4.0
XE G(I) A(N) 5.0
ND
OBJECT BOUND
LO BDQRTIC 0.0
* Solution
*LO SOLTN(100) 3.78769D+02
*LO SOLTN(500) 1.98101D+03
*LO SOLTN(1000) 3.98382D+03
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS BDQRTIC
INDIVIDUALS
T SQ
F EVAR * EVAR
G EVAR EVAR + EVAR
H EVAR EVAR 2.0
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS BDQRTIC
INDIVIDUALS
* Least squares groups
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA