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DTOC4.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME DTOC4
* Problem :
* *********
* This is a discrete time optimal control (DTOC) problem.
* The system has N time periods, 1 control variable and 2 state variables.
* The problem is not convex.
* Sources: problem 4 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 QOR2-AN-V-V
* Problem variants: they are identified by the value of the parameter N.
* The problem has 3N-1 variables (of which 2 are fixed),
* and 2(N-1) constraints
*IE N 10 $-PARAMETER n= 29,m= 18 original value
*IE N 50 $-PARAMETER n= 149,m= 98
*IE N 100 $-PARAMETER n= 299,m=198
*IE N 500 $-PARAMETER n= 1499,m=998
*IE N 1000 $-PARAMETER n= 2999,m=1998
IE N 1500 $-PARAMETER n= 4499,m=2998
*IE N 5000 $-PARAMETER n=14999,m=9998
* Constants
IA N-1 N -1
IE 1 1
IE 2 2
RI RN N
RD H RN 1.0
RM 5H H 5.0
RD 1/5H 5H 1.0
RA 1+5H 5H 1.0
RM -5H 5H -1.0
VARIABLES
DO T 1 N-1
X X(T)
OD T
DO T 1 N
X Y(T,1)
X Y(T,2)
OD T
GROUPS
* Objective function
ZN OBJ 'SCALE' 1/5H
* Transition constraints
DO T 1 N-1
IA T+1 T 1
XE TT(T,1) Y(T+1,1) -1.0
ZE TT(T,1) Y(T,1) 1+5H
ZE TT(T,1) Y(T,2) -5H
ZE TT(T,1) X(T) 5H
XE TT(T,2) Y(T+1,2) -1.0 Y(T,2) 1.0
ZE TT(T,2) Y(T,1) 5H
OD T
BOUNDS
FR DTOC4 'DEFAULT'
XX DTOC4 Y(1,1) 0.0
XX DTOC4 Y(1,2) 1.0
START POINT
XV DTOC4 Y(1,1) 0.0
XV DTOC4 Y(1,2) 1.0
ELEMENT TYPE
EV SQ Z
EV AAB A B
ELEMENT USES
XT Y1SQ(1) SQ
ZV Y1SQ(1) Z Y(1,1)
XT Y2SQ(1) SQ
ZV Y2SQ(1) Z Y(1,2)
XT XSQ(1) SQ
ZV XSQ(1) Z X(1)
DO T 2 N-1
XT Y1SQ(T) SQ
ZV Y1SQ(T) Z Y(T,1)
XT Y2SQ(T) SQ
ZV Y2SQ(T) Z Y(T,2)
XT XSQ(T) SQ
ZV XSQ(T) Z X(T)
OD T
XT Y1SQ(N) SQ
ZV Y1SQ(N) Z Y(N,1)
XT Y2SQ(N) SQ
ZV Y2SQ(N) Z Y(N,2)
DO T 1 N-1
XT E(T) AAB
ZV E(T) A Y(T,2)
ZV E(T) B Y(T,1)
OD T
GROUP USES
XE OBJ Y1SQ(1) 0.5 Y2SQ(1) 0.5
XE OBJ XSQ(1) 1.0
DO T 2 N-1
XE OBJ Y1SQ(T) Y2SQ(T)
XE OBJ XSQ(T)
OD T
XE OBJ Y1SQ(N) 0.5 Y2SQ(N) 0.5
DO T 1 N-1
ZE TT(T,1) E(T) -5H
OD T
OBJECT BOUND
LO DTOC4 0.0
*LO SOLUTION( 10) 3.75078392210
*LO SOLUTION( 50) 3.02963141755
*LO SOLUTION( 100) 2.94726711402
*LO SOLUTION( 500) 2.87827434035
*LO SOLUTION(1000) 2.87483889886
*LO SOLUTION(5000) 2.86386891514
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS DTOC4
INDIVIDUALS
T SQ
F Z * Z
G Z Z + Z
H Z Z 2.0
T AAB
F A * A * B
G A 2.0 * A * B
G B A * A
H A A B + B
H A B A + A
ENDATA