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OPTCTRL3.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME OPTCTRL3
* Problem :
* *********
* An optimal control problem
* Source:
* B. Murtagh and M. Saunders,
* Mathematical Programming studies 16, pp 84-117,
* (example 5.11)
* This problem has been modified 18 Dec 92 by Todd Plantenga as follows.
* To eliminate the active bound constraints on U1 to U9,
* a penalty term is added to the objective:
*
* mu*||u(i) - bound||
*
* By trial and error, a value of mu was found to give good
* agreement between augmented solution points and real ones,
* while maintaining the same workload on LANCELOT.
*
* New quantities are labelled with the string "TDP".
*
* Solutions for: case of T=10 case of T=40
* mu = 1E2 545.7324 719.4766
* mu = 1E3 549.5660 1347.958
* mu = 1E4 549.9565 1889.521
* mu = 1E5 2030.612
* mu = 1E6 2048.003
* mu = 1E7 2049.788
* mu = 1E8 2049.967
* mu = infinity 549.999986 2049.977124
* SIF input: Nick Gould, June 1990 and T. Plantenga December 1992.
* classification QQR2-AN-V-V
* useful parameters
*IE T 10 $-PARAMETER n = 32
*IE T 40 $-PARAMETER n = 122 original value
*IE T 100 $-PARAMETER n = 302
*IE T 400 $-PARAMETER n = 1202
IE T 1500 $-PARAMETER n = 4502
IA T-1 T -1
IE 0 0
IE 1 1
RE TDP_mu 1.0D+6
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 OPTCTRL3 x(t)
XR OPTCTRL3 y(t)
XR OPTCTRL3 u(t)
ND
XX OPTCTRL3 x(0) 10.0
XR OPTCTRL3 x(T)
XX OPTCTRL3 y(0) 0.0
XX OPTCTRL3 y(T) 0.0
START POINT
DO t 1 T-1
X OPTCTRL3 y(t) -1.0
ND
ELEMENT TYPE
EV SQR X
EV SQR_TDP X
ELEMENT USES
DO t 0 T
XT o(t) SQR
ZV o(t) X x(t)
ND
DO t 1 T-1
XT o_TDP(t) SQR_TDP
ZV o_TDP(t) X u(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 1 T-1
ZE OBJ o_TDP(t) TDP_mu
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 549.999986 (T=10)
*LO SOLTN 2049.977124 (T=40)
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS OPTCTRL3
TEMPORARIES
R X_TDP
INDIVIDUALS
* square element.
T SQR
F X * X
G X X + X
H X X 2.0
T SQR_TDP
A X_TDP X - 0.2
F X_TDP * X_TDP
G X X_TDP + X_TDP
H X X 2.0
ENDATA