Applications of convex analysis within mathematics

Title: Applications of convex analysis within mathematics
Creator: Aragón Artacho, Francisco J.; Borwein, Jonathan M.; Martín-Márquez, Victoria; Yao, Liangjin
Relation: Mathematical Programming Vol. 148, Issue 1-2, p. 49-88
Publisher Link: http://dx.doi.org/10.1007/s10107-013-0707-3
Publisher: Springer
Resource Type: journal article
Date: 2014
Description: In this paper, we study convex analysis and its theoretical applications. We first apply important tools of convex analysis to Optimization and to Analysis. We then show various deep applications of convex analysis and especially infimal convolution in Monotone Operator Theory. Among other things, we recapture the Minty surjectivity theorem in Hilbert space, and present a new proof of the sum theorem in reflexive spaces. More technically, we also discuss autoconjugate representers for maximally monotone operators. Finally, we consider various other applications in mathematical analysis.
Subject: convex function; Chebyshev set; 47B65; Fenchel conjugate; monotone operator; Fitzpatrick function; autoconjugate representer; Primary 47N10; 90C25; Secondary 47H05; 47A06
Identifier: http://hdl.handle.net/1959.13/1296093
Identifier: uon:19192
Identifier: ISSN:0025-5610
Language: eng
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