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ARWHDNE.SIF
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ARWHDNE.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME ARWHDNE
* Problem :
* *********
* A quartic problem whose Hessian is an arrow-head (downwards) with
* diagonal central part and border-width of 1.
* Nonlinear equation version of problem ARWHEAD.
* 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 NOR2-AN-V-V
* N is the number of variables
*IE N 2 $-PARAMETER
*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
XE L(I) X(I) -4.0
* The nonlinear group of the set (square)
XE G(I)
ND
CONSTANTS
* Linear groups only
DO I 1 NGS
X ARWHDNE L(I) -3.0
ND
BOUNDS
FR ARWHDNE 'DEFAULT'
START POINT
XV ARWHDNE '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 USES
* Include both squared terms in the nonlinear groups
DO I 1 NGS
XE G(I) A(I) B(I)
ND
OBJECT BOUND
* Solution
*LO SOLTN 0.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS ARWHDNE
INDIVIDUALS
* Square type element
T SQ
F V * V
G V V + V
H V V 2.0
ENDATA