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

  • 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.

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Metadaten
Author: Marcus Wagner
DOI:https://doi.org/10.1007/s10957-008-9460-9
ISSN:1573-2878
ISSN:0022-3239
Title of the source (English):Journal of Optimization Theory and Applications
Document Type:Scientific journal article peer-reviewed
Language:English
Year of publication:2009
Tag:First-order necessary conditions; Image processing; Multidimensional control problems
Volume/Year:140
Issue number:3
First Page:543
Last Page:576
Faculty/Chair:Fakultät 1 MINT - Mathematik, Informatik, Physik, Elektro- und Informationstechnik / FG Mathematik insbesondere Optimierung
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