Efficient projection onto the intersection of a half-space and a box-like set and its generalized Jacobian. (3rd April 2022)

• Record Type: Journal Article
• Authors: Wang, Bo; Lin, Lanyu; Liu, Yong-Jin
• Is Part Of: Optimization. Volume 71:Number 4(2022)
• Page Start: 1073
• Page End: 1096
• Publication Date: 2022-04-03
• Subjects: Projection -- semismooth Newton method -- generalized Jacobian; 90C20 -- 90C25; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1958810
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : This paper focuses on efficient projection onto the intersection of a half-space and a box-like set and its generalized Jacobian. Based on the Lagrangian duality theory, we deal with the projection problem via a semismooth Newton algorithm with line search safeguard, which admits global and locally quadratic convergence, to solve a univariate semismooth equation. Numerical experiments show that our proposed algorithm outperforms favourably the existing state-of-the-art standard solvers and is able to reliably solve very large-scale projection problems. Besides, we derive an explicit expression of a generalized Jacobian of the studied projection, which is an essential component of second-order nonsmooth methods.