The regularized feasible directions method for nonconvex optimization
Operations Research Letters, ISSN: 0167-6377, Vol: 50, Issue: 5, Page: 517-523
2022
- 1Citations
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Article Description
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.
Bibliographic Details
http://www.sciencedirect.com/science/article/pii/S0167637722000906; http://dx.doi.org/10.1016/j.orl.2022.07.005; http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=85135867698&origin=inward; https://linkinghub.elsevier.com/retrieve/pii/S0167637722000906; https://dx.doi.org/10.1016/j.orl.2022.07.005
Elsevier BV
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