skip to main content
Language:
Search Limited to: Search Limited to: Resource type Show Results with: Show Results with: Search type Index

Structured nonconvex and nonsmooth optimization: algorithms and iteration complexity analysis

Computational optimization and applications, 2019-01, Vol.72 (1), p.115-157 [Peer Reviewed Journal]

Springer Science+Business Media, LLC, part of Springer Nature 2018 ;Computational Optimization and Applications is a copyright of Springer, (2018). All Rights Reserved. ;ISSN: 0926-6003 ;EISSN: 1573-2894 ;DOI: 10.1007/s10589-018-0034-y

Full text available

Citations Cited by
  • Title:
    Structured nonconvex and nonsmooth optimization: algorithms and iteration complexity analysis
  • Author: Jiang, Bo ; Lin, Tianyi ; Ma, Shiqian ; Zhang, Shuzhong
  • Subjects: Algorithms ; Complexity ; Constraint modelling ; Convergence ; Convex and Discrete Geometry ; Iterative methods ; Management Science ; Mathematics ; Mathematics and Statistics ; Nonlinear programming ; Operations Research ; Operations Research/Decision Theory ; Optimization ; Robustness (mathematics) ; Statistics
  • Is Part Of: Computational optimization and applications, 2019-01, Vol.72 (1), p.115-157
  • Description: Nonconvex and nonsmooth optimization problems are frequently encountered in much of statistics, business, science and engineering, but they are not yet widely recognized as a technology in the sense of scalability. A reason for this relatively low degree of popularity is the lack of a well developed system of theory and algorithms to support the applications, as is the case for its convex counterpart. This paper aims to take one step in the direction of disciplined nonconvex and nonsmooth optimization . In particular, we consider in this paper some constrained nonconvex optimization models in block decision variables, with or without coupled affine constraints. In the absence of coupled constraints, we show a sublinear rate of convergence to an ϵ -stationary solution in the form of variational inequality for a generalized conditional gradient method, where the convergence rate is dependent on the Hölderian continuity of the gradient of the smooth part of the objective. For the model with coupled affine constraints, we introduce corresponding ϵ -stationarity conditions, and apply two proximal-type variants of the ADMM to solve such a model, assuming the proximal ADMM updates can be implemented for all the block variables except for the last block, for which either a gradient step or a majorization–minimization step is implemented. We show an iteration complexity bound of O ( 1 / ϵ 2 ) to reach an ϵ -stationary solution for both algorithms. Moreover, we show that the same iteration complexity of a proximal BCD method follows immediately. Numerical results are provided to illustrate the efficacy of the proposed algorithms for tensor robust PCA and tensor sparse PCA problems.
  • Publisher: New York: Springer US
  • Language: English
  • Identifier: ISSN: 0926-6003
    EISSN: 1573-2894
    DOI: 10.1007/s10589-018-0034-y
  • Source: AUTh Library subscriptions: ProQuest Central
Back to results list
INSPIRE LIBRARY - TON DUC THANG UNIVERSITY (84-028) 37 755 057 Feedback
19 Nguyen Huu Tho St. Dist.7, HCM thuvien@tdtu.edu.vn

Copyright © 2017 INSPIRE LIBRARY - TON DUC THANG UNIVERSITY

Searching Remote Databases, Please Wait