On self-concordant convex–concave functions
نویسندگان
چکیده
منابع مشابه
On Self-Concordant Convex-Concave Functions
In this paper, we introduce the notion of a self-concordant convex-concave function, establish basic properties of these functions and develop a path-following interior point method for approximating saddle points of “good enough” convex-concave functions – those which admit natural self-concordant convex-concave regularizations. The approach is illustrated by its applications to developing an ...
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The notion of self-concordant function on Euclidean spaces was introduced and studied by Nesterov and Nemirovsky [6]. They have used these functions to design numerical optimization algorithms based on interior-point methods ([7]). In [12], Constantin Udrişte makes an extension of this study to the Riemannian context of optimization methods. In this paper, we use a decomposable function to intr...
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We study the smooth structure of convex functions by generalizing a powerful concept so-called self-concordance introduced by Nesterov and Nemirovskii in the early 1990s to a broader class of convex functions, which we call generalized self-concordant functions. This notion allows us to develop a unified framework for designing Newton-type methods to solve convex optimization problems. The prop...
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The self-concordant-like property of a smooth convex function is a new analytical structure that generalizes the self-concordant notion. While a wide variety of important applications feature the selfconcordant-like property, this concept has heretofore remained unexploited in convex optimization. To this end, we develop a variable metric framework of minimizing the sum of a “simple” convex fun...
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We analyze the proximal Newton method for minimizing a sum of a self-concordant function and a convex function with an inexpensive proximal operator. We present new results on the global and local convergence of the method when inexact search directions are used. The method is illustrated with an application to L1-regularized covariance selection, in which prior constraints on the sparsity patt...
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ژورنال
عنوان ژورنال: Optimization Methods and Software
سال: 1999
ISSN: 1055-6788,1029-4937
DOI: 10.1080/10556789908805755