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HAGER4.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME HAGER4
* Problem :
* *********
* A nonlinear optimal control problem, by W. Hager.
* The solution given by Hager is dubious, since x(t) is not
* continuous at 1/2.
* Source: problem P4 in
* W.W. Hager,
* "Multiplier Methods for Nonlinear Optimal Control",
* SIAM J. on Numercal Analysis 27(4): 1061-1080, 1990.
* SIF input: Ph. Toint, April 1991.
* classification OLR2-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
RI 1/H N
RD H 1/H 1.0
RM H/2 H 0.5
RA 1/H-1 1/H -1.0
RM -1/H 1/H -1.0
R* 1/HSQ 1/H 1/H
RM 1/2HSQ 1/HSQ 0.5
* Constants
IE 0 0
IE 1 1
* Time dependent quantities
DO I 0 N
RI RI I
A* T(I) RI H
AM -2TI T(I) -2.0
A( Z(I) EXP -2TI
ND
DO I 0 1
AM A(I) Z(I) -0.5
AA TI+1/2 T(I) 0.5
A* B(I) A(I) TI+1/2
A* TISQ T(I) T(I)
R+ TIETC TISQ TI+1/2
A* C(I) A(I) TIETC
ND
A- DA A(1) A(0)
AM SCDA DA 0.5
A- DB B(1) B(0)
A* SCDB DB 1/H
A- DC C(1) C(0)
A* SCDC DC 1/2HSQ
* Initial state
RF E EXP 1.0
RM 3E E 3.0
RA 1+3E 3E 1.0
RS 1-E E 1.0
RM 2-2E 1-E 2.0
R/ XX0 1+3E 2-2E
VARIABLES
DO I 0 N
X X(I)
ND
DO I 1 N
X U(I)
ND
GROUPS
N OBJ
DO I 1 N
IA I-1 I -1
ZE S(I) X(I) 1/H-1
ZE S(I) X(I-1) -1/H
A( ETI EXP T(I)
RM -ETI ETI -1.0
ZE S(I) U(I) -ETI
ND
BOUNDS
FR HAGER4 'DEFAULT'
ZX HAGER4 X(0) XX0
DO I 1 N
XU HAGER4 U(I) 1.0
ND
START POINT
ZV HAGER4 X(0) XX0
ELEMENT TYPE
EV ELT X Y
EP ELT D E
EP ELT F
EV SQ X
ELEMENT USES
DO I 1 N
IA I-1 I -1
XT EL(I) ELT
ZV EL(I) X X(I)
ZV EL(I) Y X(I-1)
A* DD SCDA Z(I-1)
A* EE SCDB Z(I-1)
A* FF SCDC Z(I-1)
ZP EL(I) D DD
ZP EL(I) E EE
ZP EL(I) F FF
XT U(I)SQ SQ
ZV U(I)SQ X U(I)
ND
GROUP USES
DO I 1 N
XE OBJ EL(I)
ZE OBJ U(I)SQ H/2
ND
OBJECT BOUND
* Solution
*LO SOLTN(10) 2.833914199
*LO SOLTN(50) 2.799810928
*LO SOLTN(100) 2.796761851
*LO SOLTN(500) 2.794513229
*LO SOLTN(1000) 2.794244187
*LO SOLTN(5000) ???
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS HAGER4
INDIVIDUALS
T ELT
F D*X*X + E*X*(Y-X) + F*(Y-X)**2
G X 2.0*D*X + E*(Y-2.0*X) - 2.0*F*(Y-X)
G Y E * X + 2.0*F*(Y-X)
H X X 2.0 * ( D - E + F )
H X Y E - 2.0 * F
H Y Y 2.0 * F
T SQ
F X * X
G X X + X
H X X 2.0
ENDATA