Efficient projection onto the intersection of a half-space and a box-like set and its generalized Jacobian

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.

Keywords:

• Projection
• semismooth Newton method
• generalized Jacobian

AMS Subject Classification (2000):

• 90C20
• 90C25

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Bo Wang's research is supported in part by the National Natural Science Foundation of China [grant number 11701091], Fujian Education and Research Program for Young Teachers [grant number JAT170096]. Yong-Jin Liu's research is supported in part by the National Natural Science Foundation of China [grant number 11371255], [grant number 11871153], the Natural Science Foundation of Fujian Province, China [grant number 2019J01644].