Topological Aspects of Nonsmooth Optimization

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In applied mathematics, topological based data analysis (TDA) is an approach to the analysis of datasets using techniques from topology.Extraction of information from datasets that are high-dimensional, incomplete and noisy is generally challenging. TDA provides a general framework to analyze such data in a manner that is insensitive to the particular metric chosen and provides …
02/11/2021 · The purpose of Positivity is to provide an outlet for high quality original research in all areas of analysis and its applications to other disciplines having a clear and substantive link to the general theme of positivity. Specifically, articles that illustrate applications of positivity to other disciplines - including but not limited to - economics, engineering, life sciences, physics, …
23/12/2021 · The symposium is devoted to all aspects of finite elements and other computer-based methods for solving partial differential equations. The topics include but are not limited to: scientific computing, mechanics/applications, inverse problems and optimization with PDEs, uncertainty quantification.
In this paper, we study nonsmooth nonconvex optimization from an oracle complexity viewpoint, where the algorithm is assumed to be given access only to local information about the function at various points. We provide two main results (under mild assumptions): First, we consider the problem of getting \emph{near} ϵ -stationary points.

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