The Resolvent Order: A Unification of the Orders by Zarantonello, by Loewner, and by Moreau

DOI10.1137/16M1082172zbMath1425.47006arXiv1606.08809MaRDI QIDQ5737716

Sedi Bartz, Heinz H. Bauschke, Shawn Xianfu Wang

Publication date: 30 May 2017

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.08809

zbMATH Keywords

resolventconvex functionconvex coneprojectorenvelopepositive semidefinite matrixmaximally monotone operatorproximity operatorMoreau envelopefirmly nonexpansive mappingLoewner orderprojection mappingproximal mappingBaillon-Haddad theoremMoreau's orderresolvent orderZarantonello's order

Mathematics Subject Classification ID

Convex programming (90C25) Monotone operators and generalizations (47H05) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Convex functions and convex programs in convex geometry (52A41) Hermitian, skew-Hermitian, and related matrices (15B57) Convexity of real functions of several variables, generalizations (26B25) Convex sets and cones of operators (47L07)

Related Items (3)

Maximal Monotonicity and Cyclic Involutivity of Multiconjugate Convex Functions ⋮ Multi-marginal maximal monotonicity and convex analysis ⋮ On sums and convex combinations of projectors onto convex sets

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