Applications of convex analysis within mathematics

• 成果类型: Article
• 署名作者: Artacho, Francisco J. Aragon; Borwein, Jonathan M.; Martin-Marquez, Victoria; Yao, Liangjin
• 署名单位: University of Newcastle; King Abdulaziz University; University of Sevilla
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-013-0707-3
• 发表日期: 2014
• 页码: 49-88
• 关键词: maximal monotone-operators; reflexive banach-spaces; subdifferential calculus; fitzpatrick functions; fenchel duality; REPRESENTATION; extension; mappings; sums; sets

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.