Inexact primal–dual gradient projection methods for nonlinear optimization on convex set. (2nd October 2020)

• Record Type: Journal Article
• Authors: Zhang, Fan; Wang, Hao; Wang, Jiashan; Yang, Kai
• Is Part Of: Optimization. Volume 69:Number 10(2020)
• Page Start: 2339
• Page End: 2365
• Publication Date: 2020-10-02
• Subjects: Inexact optimization -- gradient projection methods -- ℓ1-ball projection -- first-order methods -- proximal methods; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1696338
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, we propose a novel primal–dual inexact gradient projection method for nonlinear optimization problems with convex-set constraint. This method only needs inexact computation of the projections onto the convex set for each iteration, consequently reducing the computational cost for projections per iteration. This feature is attractive especially for solving problems where the projections are computationally not easy to calculate. Global convergence guarantee and O ( 1 / k ) ergodic convergence rate of the optimality residual are provided under loose assumptions. We apply our proposed strategy to ℓ 1 -ball constrained problems. Numerical results exhibit that our inexact gradient projection methods for solving ℓ 1 -ball constrained problems are more efficient than the exact methods.