Pontryagin’s Maximum Principle for Multidimensional Control Problems in Image Processing

M. Wagner ()
Additional contact information
M. Wagner: Brandenburgische Technische Universität Cottbus

Journal of Optimization Theory and Applications, 2009, vol. 140, issue 3, No 11, 543-576

Abstract: Abstract In the present paper, we prove a substantially improved version of the Pontryagin maximum principle for convex multidimensional control problems of Dieudonné-Rashevsky type. Although the range of the operator describing the first-order PDE system involved in this problem has infinite codimension, we obtain first-order necessary conditions in a completely analogous form as in the one-dimensional case. Furthermore, the adjoint variables are subjected to a Weyl decomposition. We reformulate two basic problems of mathematical image processing (determination of optical flow and shape from shading problem) within the framework of optimal control, which gives the possibility to incorporate hard constraints in the problems. In the convex case, we state the necessary optimality conditions for these problems.

Keywords: Multidimensional control problems; Pontryagin’s principle; First-order necessary conditions; Infinite codimension; Weyl decomposition; Image processing; Optical flow; Shape from shading (search for similar items in EconPapers)
Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-008-9460-9 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:140:y:2009:i:3:d:10.1007_s10957-008-9460-9

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-008-9460-9

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().