Convergence of the Iterates in Mirror Descent Methods

Thinh T. Doan, Subhonmesh Bose, D. Hoa Nguyen, Carolyn L. Beck

    Research output: Contribution to journalArticlepeer-review

    10 Citations (Scopus)

    Abstract

    We consider centralized and distributed mirror descent (MD) algorithms over a finite-dimensional Hilbert space, and prove that the problem variables converge to an optimizer of a possibly nonsmooth function when the step sizes are square summable but not summable. Prior literature has focused on the convergence of the function value to its optimum. However, applications from distributed optimization and learning in games require the convergence of the variables to an optimizer, which is generally not guaranteed without assuming strong convexity of the objective function. We provide numerical simulations comparing entropic MD and standard subgradient methods for the robust regression problem.

    Original languageEnglish
    Pages (from-to)114-119
    Number of pages6
    JournalIEEE Control Systems Letters
    Volume3
    Issue number1
    DOIs
    Publication statusPublished - Jan 2019

    All Science Journal Classification (ASJC) codes

    • Control and Systems Engineering
    • Control and Optimization

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