Article (Scientific journals)
Applications of convex analysis within mathematics
ARAGÓN ARTACHO, Francisco Javier; Borwein, J. M.; Martín-Márquez, V. et al.
In pressIn Mathematical Programming, p. 1-40
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Keywords :
convex function; Chebyshev set; Fenchel conjugate
Abstract :
[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.
Research center :
Luxembourg Centre for Systems Biomedicine (LCSB): Systems Biochemistry (Fleming Group)
Disciplines :
Mathematics
Author, co-author :
ARAGÓN ARTACHO, Francisco Javier ;  University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB)
Borwein, J. M.
Martín-Márquez, V.
Yao, L.
Language :
English
Title :
Applications of convex analysis within mathematics
Publication date :
In press
Journal title :
Mathematical Programming
ISSN :
0025-5610
eISSN :
1436-4646
Pages :
1-40
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBilu :
since 15 November 2013

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