2021/06/24 by Anton Rodomanov, Yurii Nesterov, Rodomanov, Anton +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Sparse and Compressive Sensing Techniques #math.OC
paper · pdf · doi:10.48550/arxiv.2106.13340
arxiv created 2021/06/24 · openalex publication_date 2021/06/24 · arxiv updated 2021/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.