A new approach to improve ill-conditioned parabolic optimal control problem via time domain decomposition

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

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.

Original languageBritish English
Pages (from-to)635-666
Number of pages32
JournalNumerical Algorithms
Volume72
Issue number3
DOIs
StatePublished - 1 Jul 2016

Keywords

  • Heat control
  • Ill conditioned optimal control
  • Newton’s method
  • Steepest descent method
  • Time domain decomposition

Fingerprint

Dive into the research topics of 'A new approach to improve ill-conditioned parabolic optimal control problem via time domain decomposition'. Together they form a unique fingerprint.

Cite this