TY - JOUR
T1 - A new approach to improve ill-conditioned parabolic optimal control problem via time domain decomposition
AU - Riahi, Mohamed Kamel
N1 - Publisher Copyright:
© 2015, Springer Science+Business Media New York (outside the USA).
PY - 2016/7/1
Y1 - 2016/7/1
N2 - In this paper we present a new steepest-descent type algorithm for convex optimization problems. Our algorithm pieces the unknown into sub-blocs of unknowns and considers a partial optimization over each sub-bloc. In quadratic optimization, our method involves Newton technique to compute the step-lengths for the sub-blocs resulting descent directions. Our optimization method is fully parallel and easily implementable, we first presents it in a general linear algebra setting, then we highlight its applicability to a parabolic optimal control problem, where we consider the blocs of unknowns with respect to the time dependency of the control variable. The parallel tasks, in the last problem, turn “on” the control during a specific time-window and turn it “off” elsewhere. We show that our algorithm significantly improves the computational time compared with recognized methods. Convergence analysis of the new optimal control algorithm is provided for an arbitrary choice of partition. Numerical experiments are presented to illustrate the efficiency and the rapid convergence of the method.
AB - In this paper we present a new steepest-descent type algorithm for convex optimization problems. Our algorithm pieces the unknown into sub-blocs of unknowns and considers a partial optimization over each sub-bloc. In quadratic optimization, our method involves Newton technique to compute the step-lengths for the sub-blocs resulting descent directions. Our optimization method is fully parallel and easily implementable, we first presents it in a general linear algebra setting, then we highlight its applicability to a parabolic optimal control problem, where we consider the blocs of unknowns with respect to the time dependency of the control variable. The parallel tasks, in the last problem, turn “on” the control during a specific time-window and turn it “off” elsewhere. We show that our algorithm significantly improves the computational time compared with recognized methods. Convergence analysis of the new optimal control algorithm is provided for an arbitrary choice of partition. Numerical experiments are presented to illustrate the efficiency and the rapid convergence of the method.
KW - Heat control
KW - Ill conditioned optimal control
KW - Newton’s method
KW - Steepest descent method
KW - Time domain decomposition
UR - http://www.scopus.com/inward/record.url?scp=84944710401&partnerID=8YFLogxK
U2 - 10.1007/s11075-015-0060-0
DO - 10.1007/s11075-015-0060-0
M3 - Article
AN - SCOPUS:84944710401
SN - 1017-1398
VL - 72
SP - 635
EP - 666
JO - Numerical Algorithms
JF - Numerical Algorithms
IS - 3
ER -