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Communication Dans Un Congrès Année : 2021

Stochastic incremental mirror descent algorithms with Nesterov smoothing

Résumé

We propose a stochastic incremental mirror descent method constructed by means of the Nesterov smoothing for minimizing a sum of finitely many proper, convex and lower semicontinuous functions over a nonempty closed convex set in a Euclidean space. The algorithm can be adapted in order to minimize (in the same setting) a sum of finitely many proper, convex and lower semicontinuous functions composed with linear operators. Another modification of the scheme leads to a stochastic incremental mirror descent Bregman-proximal scheme with Nesterov smoothing for minimizing the sum of finitely many proper, convex and lower semicontinuous functions with a prox-friendly proper, convex and lower semicontinuous function in the same framework. Different to the previous contributions from the literature on mirror descent methods for minimizing sums of functions, we do not require these to be (Lipschitz) continuous or differentiable. Applications in Logistics, Tomography and Machine Learning modelled as optimization problems illustrate the theoretical achievements.
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Dates et versions

hal-04005445 , version 1 (26-02-2023)

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  • HAL Id : hal-04005445 , version 1

Citer

Sorin-Mihai Grad, Sandy Bitterlich. Stochastic incremental mirror descent algorithms with Nesterov smoothing. Workshop on Optimisation, Metric Bounds, Approximation and Transversality - WoMBaT2021, Dec 2021, Melbourne (on line), Australia. ⟨hal-04005445⟩
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