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HAGER1.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME HAGER1
* Problem :
* *********
* A nonlinear optimal control problem, by W. Hager.
* Source: problem P1 in
* W.W. Hager,
* "Multiplier Methods for Nonlinear Optimal Control",
* SIAM J. on Numercal Analysis 27(4): 1061-1080, 1990.
* SIF input: Ph. Toint, March 1991.
* classification SLR2-AN-V-V
* Number of discretized points in [0,1]
*IE N 10 $-PARAMETER original value
*IE N 50 $-PARAMETER
*IE N 100 $-PARAMETER
*IE N 500 $-PARAMETER
*IE N 1000 $-PARAMETER
IE N 2500 $-PARAMETER
*IE N 5000 $-PARAMETER
* Mesh
IA N-1 N -1
RI RN N
RD H RN 1.0
RM 2/H RN 2.0
RA 1/H-1/2 RN -0.5
RM -1/H RN -1.0
RA -1/H-1/2 -1/H -0.5
* Constants
IE 0 0
IE 1 1
VARIABLES
DO I 0 N
X X(I)
ND
DO I 1 N
X U(I)
ND
GROUPS
XN XNSQ X(N) 1.0
XN XNSQ 'SCALE' 2.0
DO I 1 N
XN U(I)SQ U(I) 1.0
ZN U(I)SQ 'SCALE' 2/H
ND
DO I 1 N
IA I-1 I -1
ZE S(I) X(I) 1/H-1/2
ZE S(I) X(I-1) -1/H-1/2
XE S(I) U(I) -1.0
ND
BOUNDS
FR HAGER1 'DEFAULT'
XX HAGER1 X(0) 1.0
START POINT
XV HAGER1 X(0) 1.0
GROUP TYPE
GV L2 GVAR
GROUP USES
XT XNSQ L2
DO I 1 N
XT U(I)SQ L2
ND
OBJECT BOUND
LO HAGER1 0.0
* Solution
*LO SOLTN(10) 0.88097222455
*LO SOLTN(50) 0.88080408397
*LO SOLTN(100) 0.88079882866
*LO SOLTN(500) 0.88079714798
*LO SOLTN(1000) 0.88079709548
*LO SOLTN(5000) 0.88079708841
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS HAGER1
* Least-square groups
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA