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DTOC6.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME DTOC6
* Problem :
* *********
* This is a discrete time optimal control (DTOC) problem.
* The system has N time periods, 1 control variable and 1 state variable.
* The problem is convex.
* Sources: problem 6 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.
* D.M. Murray and S.J. Yakowitz,
* "The application of optimal contraol methodology to nonlinear programming
* problems",
* Mathematical Programming 21, pp. 331-347, 1981.
* SIF input: Ph. Toint, August 1993
* classification OOR2-AN-V-V
* Problem variants: they are identified by the value of the parameter N.
* The problem has 2N-1 variables (of which 1 is fixed),
* and N-1 constraints
*IE N 11 $-PARAMETER n = 21, m = 10
*IE N 21 $-PARAMETER n = 41, m = 20
*IE N 31 $-PARAMETER n = 61, m = 30
*IE N 41 $-PARAMETER n = 81, m = 40
*IE N 51 $-PARAMETER n = 101, m = 50
*IE N 61 $-PARAMETER n = 121, m = 60
*IE N 71 $-PARAMETER n = 141, m = 70
*IE N 81 $-PARAMETER n = 161, m = 80
*IE N 91 $-PARAMETER n = 181, m = 90
*IE N 101 $-PARAMETER n = 201, m = 100
*IE N 501 $-PARAMETER n = 1001, m = 500
*IE N 1001 $-PARAMETER n = 2001, m =1000
IE N 5001 $-PARAMETER n =10001, m =5000
* Constants
IA N-1 N -1
IE 1 1
VARIABLES
DO T 1 N-1
X X(T)
OD T
DO T 1 N
X Y(T)
OD T
GROUPS
* Objective function
DO T 1 N-1
XN OY(T) Y(T) 1.0
XN OY(T) 'SCALE' 2.0
XN OX(T) X(T) 1.0
XN OX(T) 'SCALE' 2.0
OD T
* Transition constraints
DO T 1 N-1
IA T+1 T 1
XE TT(T) Y(T+1) -1.0 Y(T) 1.0
OD T
BOUNDS
FR DTOC6 'DEFAULT'
XX DTOC6 Y(1) 0.0
START POINT
XV DTOC6 Y(1) 0.0
ELEMENT TYPE
EV EXP Z
ELEMENT USES
DO T 1 N-1
XT E(T) EXP
ZV E(T) Z X(T)
OD T
GROUP TYPE
GV L2 GVAR
GROUP USES
DO T 1 N-1
XT OX(T) L2
XT OY(T) L2
XE OY(T) E(T)
XE TT(T) E(T)
OD T
OBJECT BOUND
LO DTOC6 0.0
*LO SOLUTION( 11) 19.80411526774
*LO SOLUTION( 21) 62.49481326823
*LO SOLUTION( 31) 119.0328455446
*LO SOLUTION( 41) 185.8961987565
*LO SOLUTION( 51) 261.1131573312
*LO SOLUTION( 61) 343.3995402405
*LO SOLUTION( 71) 431.8430677467
*LO SOLUTION( 81) 525.7575776948
*LO SOLUTION( 91) 624.6051839906
*LO SOLUTION( 101) 727.9505731659
*LO SOLUTION( 501) 6846.330143698
*LO SOLUTION(1001) 17176.03828316
*LO SOLUTION(5001)
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS DTOC6
TEMPORARIES
R EZ
M EXP
INDIVIDUALS
T EXP
A EZ EXP( Z )
F EZ
G Z EZ
H Z Z EZ
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS DTOC6
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA