(Springer, 2014-12) Aragón Artacho, Francisco Javier; Borwein, Jonathan M.; Martín Márquez, Victoria; Yao, Liangjin; Universidad de Sevilla. Departamento de Análisis Matemático; Australian Research Council; Universidad de Sevilla. FQM127: Análisis Funcional no Lineal
In this paper, we study convex analysis and its theoretical applications. We apply important tools of convex analysis to Optimization and to Analysis. Then we 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.
