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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The paper studies both the convexity and average-convexity properties for a particular class of cooperative TU-games called common pool games. The common pool situation involves a cost function as well as a (weakly decreasing) average joint production function. Firstly, it is shown that, if the relevant cost function is a linear function, then the common pool games are convex games. The convexi...
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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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ژورنال
عنوان ژورنال: Journal of Optimization Theory and Applications
سال: 2010
ISSN: 0022-3239,1573-2878
DOI: 10.1007/s10957-010-9747-5