Nonsmooth Optimization and Its Applications

Seyedehsomayeh Hosseini, Boris S. Mordukhovich, André Uschmajew

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English

Springer Nature Switzerland AG
10 April 2019

Operational research; Calculus of variations; Numerical analysis

Series: International Series of Numerical Mathematics

Since nonsmooth optimization problems arise in a diverse range of real-world applications, the potential impact of efficient methods for solving such problems is undeniable. Even solving difficult smooth problems sometimes requires the use of nonsmooth optimization methods, in order to either reduce the problem’s scale or simplify its structure. Accordingly, the field of nonsmooth optimization is an important area of mathematical programming that is based on by now classical concepts of variational analysis and generalized derivatives, and has developed a rich and sophisticated set of mathematical tools at the intersection of theory and practice.

This volume of ISNM is an outcome of the workshop ""Nonsmooth Optimization and its Applications,"" which was held from May 15 to 19, 2017 at the Hausdorff Center for Mathematics, University of Bonn. The six research articles gathered here focus on recent results that highlight different aspects of nonsmooth and variational analysis, optimization methods, their convergence theory and applications.

Edited by: Seyedehsomayeh Hosseini, Boris S. Mordukhovich, André Uschmajew
Imprint: Springer Nature Switzerland AG
Country of Publication: Switzerland
Edition: 1st ed. 2019
Volume: 170
Dimensions: Height: 235mm, Width: 155mm,
Weight: 454g
ISBN: 9783030113698
ISBN 10: 3030113698
Series: International Series of Numerical Mathematics
Pages: 149
Publication Date: 10 April 2019
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

A Collection of Nonsmooth Riemannian Optimization Problems.- An approximate ADMM for solving linearly constrained nonsmooth problems with two blocks of variables.- Tangent and normal cones for low-rank matrices.- Subdifferential enlargements and continuity properties of the VU-decomposition in convex optimization.- Proximal mappings and Moreau envelopes of single-variable convex piecewise cubic functions and multivariable gauge functions.- Newton-like dynamics associated to nonconvex optimization problems.