منابع مشابه
The Proximal Average: Basic Theory
The recently introduced proximal average of two convex functions is a convex function with many useful properties. In this paper, we introduce and systematically study the proximal average for finitely many convex functions. The basic properties of the proximal average with respect to the standard convex-analytical notions (domain, Fenchel conjugate, subdifferential, proximal mapping, epi-conti...
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The NC-proximal average is a parametrized function used to continuously transform one proper, lsc, prox-bounded function into another. Until now it has been defined for two functions. The purpose of this article is to redefine it so that any finite number of functions may be used. The layout generally follows that of [11], extending those results to the more general case and in some instances g...
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Bauschke, Lucet, and Trienis [SIAM Rev., 50 (2008), pp. 115–132] developed the concept of the proximal average of two convex functions. In this work we show the relationship between the proximal average and the Moreau envelope and exploit this relationship to develop stability theory for a generalized proximal average function. This approach allows us to extend the concept of the proximal avera...
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It is a common practice to approximate “complicated” functions with more friendly ones. In large-scale machine learning applications, nonsmooth losses/regularizers that entail great computational challenges are usually approximated by smooth functions. We re-examine this powerful methodology and point out a nonsmooth approximation which simply pretends the linearity of the proximal map. The new...
متن کاملAverage Case Complexity Theory
Informally, Average case Complexity theory considers the average complexity with respect to a probability distribution over the set of inputs, instead of the complexity on the worst case input, as a criterion for the hardness of a problem. With regard to this theory, we explore the notion of a natural distribution. In particular, we consider different bounds on the minentropy of such distributi...
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ژورنال
عنوان ژورنال: SIAM Journal on Optimization
سال: 2008
ISSN: 1052-6234,1095-7189
DOI: 10.1137/070687542