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ARWHEAD.SIF
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ARWHEAD.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME ARWHEAD
* Problem :
* *********
* A quartic problem whose Hessian is an arrow-head (downwards) with
* diagonal central part and border-width of 1.
* Source: Problem 55 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 OUR2-AN-V-0
* N is the number of variables
*IE N 100 $-PARAMETER
*IE N 500 $-PARAMETER
*IE N 1000 $-PARAMETER
IE N 5000 $-PARAMETER
* Number of groups sets: each set has a linear and a nonlinear group
IA NGS N -1
* Define useful parameters
IE 1 1
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
DO I 1 NGS
* The linear group of the set
XN L(I) X(I) -4.0
* The nonlinear group of the set (square)
XN G(I)
ND
CONSTANTS
* Linear groups only
DO I 1 NGS
X ARWHEAD L(I) -3.0
ND
BOUNDS
FR ARWHEAD 'DEFAULT'
START POINT
XV ARWHEAD 'DEFAULT' 1.0
ELEMENT TYPE
EV SQ V
ELEMENT USES
T 'DEFAULT' SQ
DO I 1 NGS
ZV A(I) V X(I)
ZV B(I) V X(N)
ND
GROUP TYPE
GV L2 GVAR
GROUP USES
* Include both squared terms in the nonlinear groups
DO I 1 NGS
XT G(I) L2
XE G(I) A(I) B(I)
ND
OBJECT BOUND
* Solution
*LO SOLTN 0.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS ARWHEAD
INDIVIDUALS
* Square type element
T SQ
F V * V
G V V + V
H V V 2.0
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS ARWHEAD
INDIVIDUALS
* Least-square root groups
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA