A stochastic primal-dual method for a class of nonconvex constrained optimization
Lingzi Jin () and
Xiao Wang ()
Additional contact information
Lingzi Jin: University of Chinese Academy of Sciences
Xiao Wang: University of Chinese Academy of Sciences
Computational Optimization and Applications, 2022, vol. 83, issue 1, No 5, 143-180
Abstract In this paper we study a class of nonconvex optimization which involves uncertainty in the objective and a large number of nonconvex functional constraints. Challenges often arise when solving this type of problems due to the nonconvexity of the feasible set and the high cost of calculating function value and gradient of all constraints simultaneously. To handle these issues, we propose a stochastic primal-dual method in this paper. At each iteration, a proximal subproblem based on a stochastic approximation to an augmented Lagrangian function is solved to update the primal variable, which is then used to update dual variables. We explore theoretical properties of the proposed algorithm and establish its iteration and sample complexities to find an $$\epsilon$$ ϵ -stationary point of the original problem. Numerical tests on a weighted maximin dispersion problem and a nonconvex quadratically constrained optimization problem demonstrate the promising performance of the proposed algorithm.
Keywords: Nonconvex optimization; Augmented Lagrangian function; Stochastic gradient; $$\epsilon$$ ϵ -stationary point; Complexity; 90C30; 90C06; 65K05; 92C15 (search for similar items in EconPapers)
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed
Downloads: (external link)
http://link.springer.com/10.1007/s10589-022-00384-w Abstract (text/html)
Access to the full text of the articles in this series is restricted.
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:spr:coopap:v:83:y:2022:i:1:d:10.1007_s10589-022-00384-w
Ordering information: This journal article can be ordered from
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 ().