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NONMSQRT.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME NONMSQRT
* Problem :
* *********
* The "non-matrix square root problem" obtained from an error in
* writing a correct matrix square root problem B by Nocedal and Liu.
* Source:
* Ph. Toint
* SIF input: Ph. Toint, Dec 1989.
* classification SUR2-AN-V-0
* Dimension of the matrix ( at least 3)
*IE P 3 $-PARAMETER n = 9 original value
*IE P 7 $-PARAMETER n = 49
*IE P 10 $-PARAMETER n = 100
*IE P 23 $-PARAMETER n = 529
*IE P 32 $-PARAMETER n = 1024
IE P 70 $-PARAMETER n = 4900
* Number of variables
I* N P P
* other parameter definitions
IE 1 1
* Define the matrix B
RE K 0.0
DO I 1 P
DO J 1 P
RA K K 1.0
R* K2 K K
A( B(I,J) SIN K2
ND
RE B3,1 0.0
* Compute A = B * B
DO I 1 P
DO J 1 P
AE A(I,J) 0.0
DO T 1 P
A* PROD B(I,T) B(T,J)
A+ A(I,J) A(I,J) PROD
ND
VARIABLES
DO I 1 P
DO J 1 P
X X(I,J)
ND
GROUPS
DO I 1 P
DO J 1 P
XN G(I,J)
ND
CONSTANTS
DO I 1 P
DO J 1 P
Z NONMSQRT G(I,J) A(I,J)
ND
BOUNDS
FR NONMSQRT 'DEFAULT'
START POINT
RE K 0.0
DO I 1 P
DO J 1 P
RA K K 1.0
R* K2 K K
R( SK2 SIN K2
RM -4SK2/5 SK2 -0.8
A+ XIJ B(I,J) -4SK2/5
Z NONMSQRT X(I,J) XIJ
ND
ELEMENT TYPE
EV 2PR XIT XTJ
ELEMENT USES
DO I 1 P
DO J 1 P
DO K 1 P
XT E(I,J,K) 2PR
ZV E(I,J,K) XIT X(I,K)
ZV E(I,J,K) XTJ X(I,J)
ND
GROUP TYPE
GV L2 GVAR
GROUP USES
DO I 1 P
DO J 1 P
XT G(I,J) L2
DO K 1 P
XE G(I,J) E(I,J,K)
ND
OBJECT BOUND
* Least square problems are bounded below by zero
LO NONMSQRT 0.0
* Solution
*LO SOLTN(3) 0.075194572
*LO SOLTN(7) ???
*LO SOLTN(10) ???
*LO SOLTN(23) 61.327
*LO SOLTN(32) ???
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS NONMSQRT
INDIVIDUALS
T 2PR
F XIT * XTJ
G XIT XTJ
G XTJ XIT
H XIT XTJ 1.0
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS NONMSQRT
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA