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HAGER3.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME HAGER3
* Problem :
* *********
* A nonlinear optimal control problem, by W. Hager.
* Source: problem P3 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-AY-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 4/H RN 4.0
RM 8/H RN 8.0
RA 1/H-1/4 RN -0.25
RM -1/H RN -1.0
RA -1/H-1/4 -1/H -0.25
* 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
DO I 1 N
ZN OX(I) 'SCALE' 8/H
XN U(I)SQ U(I) 1.0
ZN U(I)SQ 'SCALE' 4/H
ND
DO I 1 N
IA I-1 I -1
ZE S(I) X(I) 1/H-1/4
ZE S(I) X(I-1) -1/H-1/4
XE S(I) U(I) -1.0
ND
BOUNDS
FR HAGER3 'DEFAULT'
XX HAGER3 X(0) 1.0
START POINT
XV HAGER3 X(0) 1.0
ELEMENT TYPE
EV LINSQ XA XB
EV LINU XA XB
EV LINU U
IV LINU XX UU
ELEMENT USES
DO I 1 N
IA I-1 I -1
XT E(I) LINSQ
ZV E(I) XA X(I-1)
ZV E(I) XB X(I)
XT UX(I) LINU
ZV UX(I) XA X(I-1)
ZV UX(I) XB X(I)
ZV UX(I) U U(I)
ND
GROUP TYPE
GV L2 GVAR
GROUP USES
DO I 1 N
XE OX(I) E(I) 0.625 UX(I)
XT U(I)SQ L2
ND
OBJECT BOUND
* Solution
*LO SOLTN(10) 0.14103316577
*LO SOLTN(50) 0.14096413824
*LO SOLTN(100) 0.14096197328
*LO SOLTN(500) 0.14096128049
*LO SOLTN(1000) 0.14096125887
*LO SOLTN(5000) 0.14096125191
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS HAGER3
INDIVIDUALS
T LINSQ
F XA * XA + XA * XB + XB * XB
G XA 2.0 * XA + XB
G XB 2.0 * XB + XA
H XA XA 2.0
H XA XB 1.0
H XB XB 2.0
T LINU
R XX XA 1.0 XB 1.0
R UU U 1.0
F XX * UU
G XX UU
G UU XX
H XX UU 1.0
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS HAGER3
* Least-square groups
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA