A smoothing stochastic quasi-newton method for non-lipschitzian stochastic optimization problems

Farzad Yousefian, Angelia Nedic, Uday V. Shanbhag

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

Motivated by big data applications, we consider unconstrained stochastic optimization problems. Stochastic quasi-Newton methods have proved successful in addressing such problems. However, in both convex and non-convex regimes, most existing convergence theory requires the gradient mapping of the objective function to be Lipschitz continuous, a requirement that might not hold. To address this gap, we consider problems with not necessarily Lipschitzian gradients. Employing a local smoothing technique, we develop a smoothing stochastic quasi-Newton (S-SQN) method. Our main contributions are three-fold: (i) under suitable assumptions, we show that the sequence generated by the S-SQN scheme converges to the unique optimal solution of the smoothed problem almost surely; (ii) we derive an error bound in terms of the smoothed objective function values; and (iii) to quantify the solution quality, we derive a bound that relates the iterate generated by the S-SQN method to the optimal solution of the original problem.

Original languageEnglish (US)
Title of host publication2017 Winter Simulation Conference, WSC 2017
EditorsVictor Chan
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2291-2302
Number of pages12
ISBN (Electronic)9781538634288
DOIs
StatePublished - Jun 28 2017
Event2017 Winter Simulation Conference, WSC 2017 - Las Vegas, United States
Duration: Dec 3 2017Dec 6 2017

Publication series

NameProceedings - Winter Simulation Conference
ISSN (Print)0891-7736

Other

Other2017 Winter Simulation Conference, WSC 2017
Country/TerritoryUnited States
CityLas Vegas
Period12/3/1712/6/17

All Science Journal Classification (ASJC) codes

  • Software
  • Modeling and Simulation
  • Computer Science Applications

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