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Mathematics > Optimization and Control

arXiv:1812.09017 (math)
[Submitted on 21 Dec 2018]

Title:Corporative Stochastic Approximation with Random Constraint Sampling for Semi-Infinite Programming

Authors:Bo Wei, William B. Haskell, Sixiang Zhao
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Abstract:We developed a corporative stochastic approximation (CSA) type algorithm for semi-infinite programming (SIP), where the cut generation problem is solved inexactly. First, we provide general error bounds for inexact CSA. Then, we propose two specific random constraint sampling schemes to approximately solve the cut generation problem. When the objective and constraint functions are generally convex, we show that our randomized CSA algorithms achieve an $\mathcal{O}(1/\sqrt{N})$ rate of convergence in expectation (in terms of optimality gap as well as SIP constraint violation). When the objective and constraint functions are all strongly convex, this rate can be improved to $\mathcal{O}(1/N)$.
Subjects: Optimization and Control (math.OC)
Cite as: arXiv:1812.09017 [math.OC]
  (or arXiv:1812.09017v1 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.1812.09017

Submission history

From: William Haskell [view email]
[v1] Fri, 21 Dec 2018 09:40:59 UTC (449 KB)
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