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OSCIGRAD.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME OSCIGRAD
* Problem :
* *********
* The roots of the gradient of Yurii Nesterov's "oscillating path" problem
* SIF input: Nick Gould, June 2011.
* classification SUR2-AN-V-0
* Number of variables
*IE N 2 $-PARAMETER
*IE N 5 $-PARAMETER
*IE N 10 $-PARAMETER
*IE N 15 $-PARAMETER
*IE N 25 $-PARAMETER
*IE N 100 $-PARAMETER
*IE N 1000 $-PARAMETER
*IE N 10000 $-PARAMETER
IE N 100000 $-PARAMETER
* the weight factor
*RE RHO 1.0 $-PARAMETER Nesterov's original value
RE RHO 500.0 $-PARAMETER Florian Jarre's value
* other parameter definitions
IE 1 1
IE 2 2
RM 2RHO RHO 2.0
RM -4RHO RHO -4.0
IA N-1 N -1
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
N G1 X1 0.5
DO I 2 N
XN G(I)
ND
CONSTANTS
OSCIGRAD G1 0.5
BOUNDS
FR OSCIGRAD 'DEFAULT'
START POINT
XV OSCIGRAD X(1) -2.0
DO I 2 N
XV OSCIGRAD X(I) 1.0
ND
ELEMENT TYPE
EV A U
EV A V
EP A P
EV B U
EV B V
EP B P
ELEMENT USES
XT B1 B
ZV B1 V X2
ZV B1 U X1
ZP B1 P -4RHO
DO I 2 N-1
IA I-1 I -1
IA I+1 I 1
XT A(I) A
ZV A(I) V X(I)
ZV A(I) U X(I-1)
ZP A(I) P 2RHO
XT B(I) B
ZV B(I) V X(I+1)
ZV B(I) U X(I)
ZP B(I) P -4RHO
ND
XT A(N) A
ZV A(N) V X(N)
ZV A(N) U X(N-1)
ZP A(N) P 2RHO
GROUP TYPE
GV L2 GVAR
GROUP USES
T 'DEFAULT' L2
XE G1 B1 1.0
DO I 2 N-1
XE G(I) A(I) 1.0 B(I) 1.0
ND
XE G(N) A(N) 1.0
OBJECT BOUND
LO OSCIGRAD 0.0
* Solution
*LO SOLTN 0.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS OSCIGRAD
INDIVIDUALS
T A
F P * ( V - 2.0 * U ** 2 + 1.0 )
G V P
G U - 4.0 * P * U
H U U - 4.0 * P
T B
F P * ( V - 2.0 * U ** 2 + 1.0 ) * U
G V P * U
G U P * ( V - 6.0 * U ** 2 + 1.0 )
H V U P
H U U - 12.0 * P * U
ENDATA
GROUPS OSCIGRAD
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA