Nonsmooth projection-free optimization with functional constraints
Kamiar Asgari () and
Michael J. Neely ()
Additional contact information
Kamiar Asgari: University of Southern California
Michael J. Neely: University of Southern California
Computational Optimization and Applications, 2024, vol. 89, issue 3, No 11, 927-975
Abstract:
Abstract This paper presents a subgradient-based algorithm for constrained nonsmooth convex optimization that does not require projections onto the feasible set. While the well-established Frank–Wolfe algorithm and its variants already avoid projections, they are primarily designed for smooth objective functions. In contrast, our proposed algorithm can handle nonsmooth problems with general convex functional inequality constraints. It achieves an $$\epsilon $$ ϵ -suboptimal solution in $$\mathcal {O}(\epsilon ^{-2})$$ O ( ϵ - 2 ) iterations, with each iteration requiring only a single (potentially inexact) Linear Minimization Oracle call and a (possibly inexact) subgradient computation. This performance is consistent with existing lower bounds. Similar performance is observed when deterministic subgradients are replaced with stochastic subgradients. In the special case where there are no functional inequality constraints, our algorithm competes favorably with a recent nonsmooth projection-free method designed for constraint-free problems. Our approach utilizes a simple separation scheme in conjunction with a new Lagrange multiplier update rule.
Keywords: Projection-free optimization; Frank–Wolfe method; Nonsmooth convex optimization; Stochastic optimization; Functional constraints; 65K05; 65K10; 65K99; 90C25; 90C15; 90C30 (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:
Downloads: (external link)
http://link.springer.com/10.1007/s10589-024-00607-2 Abstract (text/html)
Access to the full text of the articles in this series is restricted.
Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:spr:coopap:v:89:y:2024:i:3:d:10.1007_s10589-024-00607-2
Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589
DOI: 10.1007/s10589-024-00607-2
Access Statistics for this article
Computational Optimization and Applications is currently edited by William W. Hager
More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().