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HILBERTA.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME HILBERTA
* Problem :
* *********
* The Hilbert quadratic
* Source:
* K. Schittkowski,
* "More Test Examples for Nonlinear Programming Codes",
* Springer Verlag, Heidelberg, 1987.
* See also Buckley#19 (p. 59)
* SIF input: Ph. Toint, Dec 1989.
* classification QUR2-AN-V-0
* Dimension of the problem
IE N 2 $-PARAMETER Schittkowski 274
*IE N 4 $-PARAMETER Schittkowski 275
*IE N 5 $-PARAMETER Buckley 19
*IE N 6 $-PARAMETER Schittkowski 276
*IE N 10 $-PARAMETER
* Conditioning parameter
RE D 0.0 $-PARAMETER
* Other parameters
IE 1 1
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
DO I 1 N
DO J 1 I
XN G(I,J)
ND
BOUNDS
FR HILBERTA 'DEFAULT'
START POINT
XV HILBERTA 'DEFAULT' -3.0
ELEMENT TYPE
EV 2PR X Y
EV SQ X
ELEMENT USES
DO I 1 N
IA I-1 I -1
DO J 1 I-1
XT E(I,J) 2PR
ZV E(I,J) X X(I)
ZV E(I,J) Y X(J)
OD J
XT E(I,I) SQ
ZV E(I,I) X X(I)
ND
GROUP USES
DO I 1 N
IA I-1 I -1
DO J 1 I-1
I+ I+J I J
IA I+J-1 I+J -1
RI RINVH I+J-1
RD HIJ RINVH 1.0
ZE G(I,J) E(I,J) HIJ
OD J
IM 2I I 2
IA 2I-1 2I -1
RI RH0 2I-1
RD HII RH0 1.0
RM HII/2 HII 0.5
R+ COEFF HII/2 D
ZE G(I,I) E(I,I) COEFF
ND
OBJECT BOUND
* Solution
*LO SOLTN 0.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS HILBERTA
INDIVIDUALS
T 2PR
F X * Y
G X Y
G Y X
H X Y 1.0
T SQ
F X * X
G X X + X
H X X 2.0
ENDATA