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OPTCNTRL.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME OPTCNTRL
* Problem :
* *********
* An optimal control problem
* Source:
* B. Murtagh and M. Saunders,
* Mathematical Programming studies 16, pp 84-117,
* (example 5.11)
* SIF input: Nick Gould, June 1990.
* classification QQR2-AN-32-20
* useful parameters
IE T 10
IA T-1 T -1
IE 0 0
IE 1 1
VARIABLES
DO t 0 T
X x(t)
X y(t)
ND
DO t 0 T-1
X u(t)
ND
GROUPS
N OBJ
DO t 0 T-1
IA t+1 t 1
XE B(t) x(t+1) 1.0 x(t) -1.0
XE B(t) y(t) -0.2
XE C(t) y(t+1) 1.0 y(t) -1.0
XE C(t) x(t) 0.004 u(t) -0.2
ND
BOUNDS
DO t 0 T-1
XR OPTCNTL x(t)
XL OPTCNTL y(t) -1.0
XL OPTCNTL u(t) -0.2
XU OPTCNTL u(t) 0.2
ND
XX OPTCNTL x(0) 10.0
XX OPTCNTL y(0) 0.0
XX OPTCNTL y(T) 0.0
START POINT
DO t 1 T-1
X OPTCNTL y(t) -1.0
ND
ELEMENT TYPE
EV SQR X
ELEMENT USES
DO t 0 T
XT o(t) SQR
ZV o(t) X x(t)
ND
DO t 0 T-1
XT c(t) SQR
ZV c(t) X y(t)
ND
GROUP USES
DO t 0 T
XE OBJ o(t) 0.5
ND
DO t 0 T-1
XE C(t) c(t) 0.01
ND
OBJECT BOUND
* Least square problems are bounded below by zero
LO OPTCNTL 0.0
* Solution
*LO SOLTN 549.9999869
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS OPTCNTRL
INDIVIDUALS
* square element.
T SQR
F X * X
G X X + X
H X X 2.0
ENDATA