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DTOC5.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME DTOC5
* 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 5 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.
* G. Di Pillo, L. Grippo and F. Lampariello,
* "A class of structures quasi-Newton algorithms for optimal control
* problems",
* in H.E. Rauch, ed., IFAC Applications of nonlinear programming to
* optimization and control, pp. 101-107, IFAC, Pergamon Press, 1983.
* SIF input: Ph. Toint, August 1993
* classification QQR2-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 10 $-PARAMETER n = 19, m = 9
*IE N 50 $-PARAMETER n = 99, m = 49
*IE N 100 $-PARAMETER n = 199, m = 99
*IE N 500 $-PARAMETER n = 999, m = 499
*IE N 1000 $-PARAMETER n = 1999, m = 999
IE N 5000 $-PARAMETER n = 9999, m = 4999
* Constants
IA N-1 N -1
IE 1 1
RI RN N
RD H RN 1.0
RM -H H -1.0
VARIABLES
DO T 1 N-1
X X(T)
OD T
DO T 1 N
X Y(T)
OD T
GROUPS
* Objective function
ZN OBJ 'SCALE' RN
* Transition constraints
DO T 1 N-1
IA T+1 T 1
XE TT(T) Y(T+1) -1.0 Y(T) 1.0
ZE TT(T) X(T) -H
OD T
BOUNDS
FR DTOC5 'DEFAULT'
XX DTOC5 Y(1) 1.0
START POINT
XV DTOC5 Y(1) 1.0
ELEMENT TYPE
EV SQ Z
ELEMENT USES
DO T 1 N-1
XT YSQ(T) SQ
ZV YSQ(T) Z Y(T)
XT XSQ(T) SQ
ZV XSQ(T) Z X(T)
OD T
GROUP USES
DO T 1 N-1
XE OBJ YSQ(T) XSQ(T)
ZE TT(T) YSQ(T) H
OD T
OBJECT BOUND
LO DTOC5 0.0
*LO SOLUTION( 10) 1.451893900588
*LO SOLUTION( 50) 1.528586458855
*LO SOLUTION( 100) 1.532552633518
*LO SOLUTION( 500) 1.530860973890
*LO SOLUTION(1000) 1.527434119271
*LO SOLUTION(5000) 1.531611890390
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS DTOC5
INDIVIDUALS
T SQ
F Z * Z
G Z Z + Z
H Z Z 2.0
ENDATA