# Research Seminar Series in Statistics and Mathematics

Wirtschaftsuniversität Wien , Departments 4 D4.4.008 09:00 - 10:30

Type Lecture / discussion
LanguageEnglish
SpeakerRadu Ioan Boţ (Faculty of Mathematics, University of Vienna)
Organizer Institut für Statistik und Mathematik
Contact katrin.artner@wu.ac.at

Radu Ioan Boţ (Faculty of Mathematics, University of Vienna) about "Proximal algorithms for nonconvex and nonsmooth minimization problems"

The Institute for Statistics and Mathematics (Department of Finance, Accounting and Statistics) cordially invites everyone interested to attend the talks in our Research Seminar Series, where internationally renowned scholars from leading universities present and discuss their (working) papers.
No registration required.

The list of talks for the summer term 2019 is available via the following link: https://www.wu.ac.at/en/statmath/resseminar

Abstract:
In this talk, we discuss proximal algorithms for nonconvex and nonsmooth minimization problems. We begin with a short survey of the convergence results of the proximal-gradient algorithm for convex optimization problems. Further, we introduce a proximal-gradient algorithm with inertial and memory effects for the minimization of the sum of a proper and lower semicontinuous function with a possibly nonconvex smooth function. We prove that the sequence of iterates converges to a critical point of the objective, provided that a regularization of the latter function satisfies the Kurdyka-Łojasiewicz property. This applies to semialgebraic, real subanalytic, uniformly convex and convex functions satisfying a growth condition. In the last part of the talk we propose an algorithm for solving d.c. (difference-convex) optimization problems which allows the evaluation of both the concave and the convex part by their proximal points. Additionally, we allow a smooth part, which is evaluated via its gradient. For this algorithm we show the connection to the Toland dual problem and that a descent property for the objective function of a primal-dual formulation of the problem holds. Convergence of the iterates is guaranteed, if this objective function satisfies the Kurdyka-Łojasiewicz property.

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