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UNION OF BULGARIAN MATHEMATICIANS
INSTITUTE OF MATHEMATICS AND INFORMATICS, BULGARIAN ACADEMY OF SCIENCES


 

NATIONAL MATHEMATICS COLLOQUIUM

The next meeting of the National Mathematics Colloquium will be held on June 5, 2019 (Wednesday) at 16:15 in the Conference Room of the Institute of Mathematics and Informatics, Acad. G. Bonchev Street, Block 8

A talk on:

Optimization theory: a view from variational analysis
(with emphasis on the optimal control theory)

will be delivered by Professor Emeritus Alexander Ioffe, Technion – Israel Institute of Technology, Haifa, Israel..

Everybody is invited.

Head of the Colloquium: Acad. P. Popivanov

Abstract.  Next year there will be the 60s anniversary of publication of the book of Pontryagin et al “Mathematical theory of optimal processes”. The book triggered a series of extensive studies aimed at finding general approaches to analysis of necessary conditions in constrained optimization. (Just mention the method of variations of Dubovitskii and Milyutin and controllability based approach developed in a series of publications by Gamkrelidze, Warga nd Clarke.) In the talk we shall discuss a totally new approach, possible in the framework of variational analysis. This approach is based on some ideas associated with the concept of metric regularity. Its key element is a reduction of the original constrained problem to unconstrained minimization of (necessarily nonsmooth) functionals. We shall briefly sketch a proof of Pontryagin’s maximum principle based on this approach as well as a proof of a new second order necessary condition for a strong minimum in optimal control.