The regularized feasible directions method for nonconvex optimization

Amir Beck*, Nadav Hallak

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

This paper develops and studies a feasible directions approach for the minimization of a continuous function over linear constraints in which the update directions belong to a predetermined finite set spanning the feasible set. These directions are recurrently investigated in a cyclic semi-random order, where the stepsize of the update is determined via univariate optimization. We establish that any accumulation point of this optimization procedure is a stationary point of the problem, meaning that the directional derivative in any feasible direction is nonnegative. To assess and establish a rate of convergence, we develop a new optimality measure that acts as a proxy for the stationarity condition, and substantiate its role by showing that it is coherent with first-order conditions in specific scenarios. Finally we prove that our method enjoys a sublinear rate of convergence of this optimality measure in expectation.

Original languageEnglish
Pages (from-to)517-523
Number of pages7
JournalOperations Research Letters
Volume50
Issue number5
DOIs
StatePublished - Sep 2022

Funding

FundersFunder number
Israel Science Foundation637/21, 926/21

    Keywords

    • Constrained optimization
    • Convergence analysis
    • Feasible directions
    • Nonconvex optimization
    • Nonsmooth optimization

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