Reference : Applications of convex analysis within mathematics
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Applications of convex analysis within mathematics
Aragón Artacho, Francisco Javier mailto [University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > >]
Borwein, J. M. [> >]
Martín-Márquez, V. [> >]
Yao, L. [> >]
In press
Mathematical Programming
[en] convex function ; Chebyshev set ; Fenchel conjugate
[en] 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.
Luxembourg Centre for Systems Biomedicine (LCSB): Systems Biochemistry (Fleming Group)

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