Mathematics > Optimization and Control
[Submitted on 7 Oct 2022 (v1), last revised 12 May 2024 (this version, v2)]
Title:Gradient-Type Methods For Decentralized Optimization Problems With Polyak-Łojasiewicz Condition Over Time-Varying Networks
View PDF HTML (experimental)Abstract:This paper focuses on the decentralized optimization (minimization and saddle point) problems with objective functions that satisfy Polyak-Łojasiewicz condition (PL-condition). The first part of the paper is devoted to the minimization problem of the sum-type cost functions. In order to solve a such class of problems, we propose a gradient descent type method with a consensus projection procedure and the inexact gradient of the objectives. Next, in the second part, we study the saddle-point problem (SPP) with a structure of the sum, with objectives satisfying the two-sided PL-condition. To solve such SPP, we propose a generalization of the Multi-step Gradient Descent Ascent method with a consensus procedure, and inexact gradients of the objective function with respect to both variables. Finally, we present some of the numerical experiments, to show the efficiency of the proposed algorithm for the robust least squares problem.
Submission history
From: Ilya Kuruzov [view email][v1] Fri, 7 Oct 2022 20:37:48 UTC (483 KB)
[v2] Sun, 12 May 2024 13:03:23 UTC (1,135 KB)
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