A new accelerated gradient-based estimating sequence technique for solving large-scale optimization problems with composite structure

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingsScientificpeer-review

Abstract

Various problems arising in control and data analysis can be formulated as large-scale convex optimization problems with a composite objective structure. Within the black-box optimization framework, such problems are typically solved by using accelerated first-order methods. The celebrated examples of such methods are the Fast Gradient Method and the Accelerated Multistep Gradient Method, designed by using the estimating sequences framework. In this work, we present a new class of estimating sequences, which are constructed by making use of a tighter lower bound on the objective function together with the gradient mapping technique. Based on the newly introduced estimating sequences, we construct a new method, which is also equipped with an efficient line-search strategy that provides robustness to the imperfect knowledge of the Lipschitz constant. Our proposed method enjoys the accelerated convergence rate, and our theoretical results are corroborated by numerical experiments conducted on real-world datasets. The experimental results also demonstrate the robustness of the initialization of the proposed method to the imperfect knowledge of the strong convexity parameter of the objective function.
Original languageEnglish
Title of host publication2022 IEEE 61st Conference on Decision and Control (CDC)
PublisherIEEE
Pages7516-7521
Number of pages6
ISBN (Electronic)978-1-6654-6761-2
DOIs
Publication statusPublished - 10 Jan 2023
MoE publication typeA4 Conference publication
EventIEEE Conference on Decision and Control - Cancun, Mexico, Cancun, Mexico
Duration: 6 Dec 20229 Dec 2022
Conference number: 61

Publication series

NameProceedings of the IEEE Conference on Decision & Control
ISSN (Electronic)2576-2370

Conference

ConferenceIEEE Conference on Decision and Control
Abbreviated titleCDC
Country/TerritoryMexico
CityCancun
Period06/12/202209/12/2022

Keywords

  • Gradient methods
  • Data analysis
  • Closed box
  • Linear programming
  • Robustness
  • Convex functions
  • Optimization

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