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INDEF.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME INDEF
* Problem :
* *********
* A nonconvex problem which has an indefinite Hessian at
* the starting point.
* SIF input: Nick Gould, Oct 1992.
* classification OUR2-AN-V-0
* The number of variables is N.
*IE N 10 $-PARAMETER
*IE N 50 $-PARAMETER
*IE N 100 $-PARAMETER
*IE N 1000 $-PARAMETER original value
IE N 5000 $-PARAMETER
* The parameter ALPHA controls the indefiniteness.
* Larger values of ALPHA give more indefiniteness.
RE ALPHA 0.5 $-PARAMETER indefiniteness
*RE ALPHA 1.0 $-PARAMETER
*RE ALPHA 10.0 $-PARAMETER
*RE ALPHA 100.0 $-PARAMETER
*RE ALPHA 1000.0 $-PARAMETER
* Other parameters
IE 1 1
IE 2 2
IA N-1 N -1
IA N+1 N 1
RI RN+1 N+1
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
DO I 1 N
XN L2(I) X(I) 1.0
ND
DO I 2 N-1
XN COS(I) X(I) 2.0 X(N) -1.0
XN COS(I) X(1) -1.0
ND
BOUNDS
FR INDEF 'DEFAULT'
START POINT
* start with X(I) = I/N+1.
DO I 1 N
RI RI I
R/ T RI RN+1
ZV INDEF1 X(I) T
ND
V INDEF2 'DEFAULT' 1000.0
GROUP TYPE
GV L2 GVAR
GV COS GVAR
GP COS ALPHA
GROUP USES
*T 'DEFAULT' L2
DO I 2 N-1
XT COS(I) COS
ZP COS(I) ALPHA ALPHA
ND
OBJECT BOUND
* Solution
*LO SOLTN ??
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS INDEF
TEMPORARIES
*R EXPG
*M EXP
M COS
M SIN
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
*T E2
*A EXPG EXP( GVAR * GVAR )
*F EXPG
*G 2.0D+0 * GVAR * EXPG
*H ( 4.0D+0 * GVAR * GVAR + 2.0D+0 ) * EXPG
T COS
F ALPHA * COS( GVAR )
G - ALPHA * SIN( GVAR )
H - ALPHA * COS( GVAR )
ENDATA