Primal Subgradient Methods with Predefined Step Sizes

Yurii Nesterov ()
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Yurii Nesterov: Catholic University of Louvain (UCL)

Journal of Optimization Theory and Applications, 2024, vol. 203, issue 3, No 1, 2083-2115

Abstract: Abstract In this paper, we suggest a new framework for analyzing primal subgradient methods for nonsmooth convex optimization problems. We show that the classical step-size rules, based on normalization of subgradient, or on knowledge of the optimal value of the objective function, need corrections when they are applied to optimization problems with constraints. Their proper modifications allow a significant acceleration of these schemes when the objective function has favorable properties (smoothness, strong convexity). We show how the new methods can be used for solving optimization problems with functional constraints with a possibility to approximate the optimal Lagrange multipliers. One of our primal-dual methods works also for unbounded feasible set.

Keywords: Convex optimization; Nonsmooth optimization; Subgradient methods; Constrained problems; Optimal Lagrange multipliers (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02456-9

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