Nonsmooth Optimization and Its Applications

Description

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. Front Matter ....Pages i-vii A Collection of Nonsmooth Riemannian Optimization Problems (P.-A. Absil, S. Hosseini)....Pages 1-15 An Approximate ADMM for Solving Linearly Constrained Nonsmooth Optimization Problems with Two Blocks of Variables (Adil M. Bagirov, Sona Taheri, Fusheng Bai, Zhiyou Wu)....Pages 17-44 Tangent and Normal Cones for Low-Rank Matrices (Seyedehsomayeh Hosseini, D. Russell Luke, André Uschmajew)....Pages 45-53 Subdifferential Enlargements and Continuity Properties of the \(\mathcal { {VU}}\)-Decomposition in Convex Optimization (Shuai Liu, Claudia Sagastizábal, Mikhail Solodov)....Pages 55-87 Proximal Mappings and Moreau Envelopes of Single-Variable Convex Piecewise Cubic Functions and Multivariable Gauge Functions (C. Planiden, X. Wang)....Pages 89-130 Newton-Like Dynamics Associated to Nonconvex Optimization Problems (Radu Ioan Boţ, Ernö Robert Csetnek)....Pages 131-149