Subgradient Ellipsoid Method for Nonsmooth Convex Problems
In this paper, we present a new ellipsoid-type algorithm for solving nonsmooth problems with convex structure. Examples of such problems include nonsmooth convex minimization problems, convex-concave saddle-point problems and variational inequalities with monotone operator. Our algorithm can be seen...
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Zusammenfassung: | In this paper, we present a new ellipsoid-type algorithm for solving
nonsmooth problems with convex structure. Examples of such problems include
nonsmooth convex minimization problems, convex-concave saddle-point problems
and variational inequalities with monotone operator. Our algorithm can be seen
as a combination of the standard Subgradient and Ellipsoid methods. However, in
contrast to the latter one, the proposed method has a reasonable convergence
rate even when the dimensionality of the problem is sufficiently large. For
generating accuracy certificates in our algorithm, we propose an efficient
technique, which ameliorates the previously known recipes. |
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DOI: | 10.48550/arxiv.2106.13340 |