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DTOC1NA.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME DTOC1NA
* Problem :
* *********
* This is a discrete time optimal control (DTOC) problem.
* The system has N time periods, NX control variables and NY state variables.
* The nonlinearity parameter mu is set to 0.005.
* The problem is not convex.
* Sources: problem 1 in
* T.F. Coleman and A. Liao,
* "An Efficient Trust Region Method for Unconstrained Discret-Time Optimal
* Control Problems",
* Tech. Report, ctc93tr144, Advanced Computing Research Institute,
* Cornell University, 1992.
* L.Z. Liao and C.A. Shoemaker,
* "Advantages of differential dynamic programming over Newton's method for
* discrete-time optimal control problems",
* Tech. Report ctc92tr97, Advanced Computing Research Institute,
* Cornell University, 1992.
* SIF input: Ph. Toint, August 1993
* classification OQR2-AN-V-V
* Problem variants: they are identified by the values of
* the parameter vector ( N, NX, NY )
* The problem has (N-1)*NX+N*NY variables (of which NY are fixed),
* and (N-1)*NY constraints
*IE N 10 $-PARAMETER # periods } original value
*IE NX 2 $-PARAMETER # controls } n= 58, m= 36
*IE NY 4 $-PARAMETER # states }
*IE N 50 $-PARAMETER # periods }
*IE NX 2 $-PARAMETER # controls } n= 298, m= 196
*IE NY 4 $-PARAMETER # states }
*IE N 100 $-PARAMETER # periods }
*IE NX 2 $-PARAMETER # controls } n= 598, m= 396
*IE NY 4 $-PARAMETER # states }
*IE N 500 $-PARAMETER # periods }
*IE NX 2 $-PARAMETER # controls } n= 2998, m=1996
*IE NY 4 $-PARAMETER # states }
IE N 1000 $-PARAMETER # periods }
IE NX 2 $-PARAMETER # controls } n= 5998, m=3996
IE NY 4 $-PARAMETER # states }
*IE N 10 $-PARAMETER # periods }
*IE NX 5 $-PARAMETER # controls } n= 145, m= 90
*IE NY 10 $-PARAMETER # states }
*IE N 50 $-PARAMETER # periods }
*IE NX 5 $-PARAMETER # controls } n= 745, m= 490
*IE NY 10 $-PARAMETER # states }
*IE N 100 $-PARAMETER # periods }
*IE NX 5 $-PARAMETER # controls } n= 1495, m= 990
*IE NY 10 $-PARAMETER # states }
*IE N 500 $-PARAMETER # periods }
*IE NX 5 $-PARAMETER # controls } n= 7495, m=4990
*IE NY 10 $-PARAMETER # states }
*IE N 1000 $-PARAMETER # periods }
*IE NX 5 $-PARAMETER # controls } n=14995, m=9990
*IE NY 10 $-PARAMETER # states }
* Nonlinearity parameter
RE MU 0.005 $-PARAMETER nonlinearity
* Constants
IA N-1 N -1
IE 0 0
IE 1 1
IE 2 2
IA NY-1 NY -1
I+ NX+NY NX NY
RI RXY NX+NY
RD 1/RXY RXY 1.0
R* MU/RXY MU 1/RXY
I* NYNX NX NY
IA NYNX-1 NYNX -1
* Build the transition matrices B and C
DO J 1 NX
DO I 1 NY
I- I-J I J
RI RI-J I-J
A* B(I,J) RI-J 1/RXY
I+ I+J I J
RI RI+J I+J
A* C(I,J) RI+J MU/RXY
OD J
OD I
VARIABLES
DO T 1 N-1
DO I 1 NX
X X(T,I)
OD I
OD T
DO T 1 N
DO I 1 NY
X Y(T,I)
OD I
OD T
GROUPS
* Objective function
DO T 1 N-1
DO I 1 NX
XN OX(T,I) X(T,I) 1.0
OD I
OD T
DO T 1 N
DO I 1 NY
XN OY(T,I) Y(T,I) 1.0
OD I
OD T
* Transition constraints
DO T 1 N-1
IA T+1 T 1
* First state
XE TT(T,1) Y(T+1,1) -1.0
XE TT(T,1) Y(T,1) 0.5 Y(T,2) 0.25
DO I 1 NX
ZE TT(T,1) X(T,I) B(1,I)
OD I
* Middle states
DO J 2 NY-1
IA J-1 J -1
IA J+1 J 1
XE TT(T,J) Y(T+1,J) -1.0 Y(T,J) 0.5
XE TT(T,J) Y(T,J-1) -0.25 Y(T,J+1) 0.25
DO I 1 NX
ZE TT(T,J) X(T,I) B(J,I)
OD I
OD J
* Last state
XE TT(T,NY) Y(T+1,NY) -1.0
XE TT(T,NY) Y(T,NY) 0.5 Y(T,NY-1) -0.25
DO I 1 NX
ZE TT(T,NY) X(T,I) B(NY,I)
OD I
OD T
CONSTANTS
DO T 1 N-1
DO I 1 NX
X DTOC1NA OX(T,I) -0.5
OD I
OD T
DO T 1 N
DO I 1 NY
X DTOC1NA OY(T,I) -0.25
OD I
OD T
BOUNDS
FR DTOC1NA 'DEFAULT'
DO I 1 NY
XX DTOC1NA Y(1,I) 0.0
OD I
ELEMENT TYPE
EV PR X Y
EP PR MUC
ELEMENT USES
DO T 1 N-1
DO K 0 NYNX-1
I/ I K NX
I* INX I NX
I- J K INX
IA I I 1
IA J J 1
XT E(T,K) PR
ZV E(T,K) Y Y(T,I)
ZV E(T,K) X X(T,J)
ZP E(T,K) MUC C(I,J)
OD K
OD T
GROUP TYPE
GV L4 GVAR
GROUP USES
DO T 1 N-1
DO I 1 NX
XT OX(T,I) L4
OD I
OD T
DO T 1 N
DO I 1 NY
XT OY(T,I) L4
OD I
OD T
DO T 1 N-1
DO J 1 NY
DO K 0 NYNX-1
XE TT(T,J) E(T,K)
OD K
OD J
OD T
OBJECT BOUND
LO DTOC1NA 0.0
*LO S( 10,2, 4) 0.07531263517
*LO S( 50,2, 4) 0.23949933830
*LO S( 100,2, 4) 0.44472956731
*LO S( 500,2, 4) 2.08660731072
*LO S(1000,2, 4) 4.13895890755
*LO S( 10,5,10) 1.16782170926
*LO S( 50,5,10) 6.29429519092
*LO S( 100,5,10) 12.7020120922
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS DTOC1NA
INDIVIDUALS
T PR
F MUC * X * Y
G X MUC * Y
G Y MUC *X
H X Y MUC
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS DTOC1NA
INDIVIDUALS
T L4
F GVAR**4
G 4.0 * GVAR**3
H 12.0 * GVAR**2
ENDATA