Applications of convex analysis within mathematics

被引：8

作者：

Artacho, Francisco J. Aragon ^{[1
]}

Borwein, Jonathan M. ^{[1
,2
]}

Martin-Marquez, Victoria ^{[3
]}

Yao, Liangjin ^{[1
]}

机构：

[1] Univ Newcastle, Ctr Comp Assisted Res Math & Its Applicat CARMA, Callaghan, NSW 2308, Australia

[2] King Abdulaziz Univ, Jeddah 21413, Saudi Arabia

[3] Univ Seville, Fac Matemat, Dept Anal Matemat, E-41080 Seville, Spain

来源：

MATHEMATICAL PROGRAMMING | 2014年 / 148卷 / 1-2期

基金：

澳大利亚研究理事会;

关键词：

Convex function; Chebyshev set; Fenchel conjugate; Monotone operator; Fitzpatrick function; Autoconjugate representer; MAXIMAL MONOTONE-OPERATORS; REFLEXIVE BANACH-SPACES; SUBDIFFERENTIAL CALCULUS; FITZPATRICK FUNCTIONS; FENCHEL DUALITY; REPRESENTATION; EXTENSION; MAPPINGS; SUMS; SETS;

D O I：

10.1007/s10107-013-0707-3

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

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.

引用

页码：49 / 88

页数：40

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