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Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization
Dan Butnariu,Alfredo N. Iusem +1 more
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In this paper, the authors propose a totally convex function for infinite dimensional optimization, where fixed points can be computed by infinite dif-ferentially optimising fixed points.Abstract:
Introduction. 1. Totally Convex Functions. 2. Computation of Fixed Points. 3. Infinite Dimensional Optimization. Bibliography. Index.read more
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Update or Wait: How to Keep Your Data Fresh
TL;DR: In this paper, the authors study how to optimally manage the freshness of information updates sent from a source node to a destination via a channel and develop efficient algorithms to find the optimal update policy among all causal policies and establish sufficient and necessary conditions for the optimality of the zero-wait policy.
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The Hybrid Steepest Descent Method for the Variational Inequality Problem over the Intersection of Fixed Point Sets of Nonexpansive Mappings
TL;DR: The hybrid steepest descent (HST) method as mentioned in this paper is a simple algorithmic solution to the variational inequality problem defined over the nonempty intersection of multiple fixed point sets of nonexpansive mappings in a real Hilbert space.
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A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators
TL;DR: In this article, the authors show that violations of the smoothness assumptions of the operator do not necessarily affect the convergence rate negatively, and they take this observation and weaken the smoothing assumptions on the operator and prove a novel convergence rate result.
Book
Convex Functions: Constructions, Characterizations and Counterexamples
TL;DR: Convexity is a natural and powerful property of functions that plays a significant role in many areas of mathematics, both pure and applied as mentioned in this paper, and is an important tool in optimization, mathematical programming and game theory.
Journal ArticleDOI
Essential smoothness, essential strict convexity, and legendre functions in banach spaces
TL;DR: In this article, the authors extended the notions of essential smoothness, essential strict convexity, and Legendreness for convex functions from Euclidean to Banach spaces and proved that every Legendre function on a reflexive Banach space is zone consistent.