Applications of Convex Analysis within Mathematics

2013/02/08 by Artacho, Francisco J. Aragón, Borwein, Jonathan M., Martín-Márquez, Victoria +1
#47A06 #47B65 #90C25 #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Control (math.OC) #Primary 47N10 #Secondary 47H05

paper · doi:10.48550/arxiv.1302.1978

Abstract

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.

Related

• Monotone Operator Theory in Convex Optimization
• Multi-marginal maximal monotonicity and convex analysis
• Geometric properties of maximal monotone operators and convex functions which may represent them
• A study of convex convex-composite functions via infimal convolution\n with applications
• Location, identification, and representability of monotone operators in locally convex spaces