Applications of convex analysis within mathematics

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• 作者：Francisco J. Aragón Artacho (1)
  Jonathan M. Borwein (1) (2)
  Victoria Martín-Márquez (3)
  Liangjin Yao (1)
  
• 关键词：Convex function ; Chebyshev set ; Fenchel conjugate ; Monotone operator ; Fitzpatrick function ; Autoconjugate representer ; Primary 47N10 ; 90C25 ; Secondary 47H05 ; 47A06 ; 47B65
• 刊名：Mathematical Programming
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：148
• 期：1-2
• 页码：49-88
• 全文大小：501 KB
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• 作者单位：Francisco J. Aragón Artacho (1)
  Jonathan M. Borwein (1) (2)
  Victoria Martín-Márquez (3)
  Liangjin Yao (1)
  
  1. Centre for Computer Assisted Research Mathematics and Its Applications (CARMA), University of Newcastle, Callaghan, NSW, 2308, Australia
  2. King Abdul-Aziz University, Jeddah, Saudi Arabia
  3. Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, PO Box 1160, 41080?, Sevilla, Spain
  
• ISSN：1436-4646

文摘

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.