An inertial relaxed CQ algorithm with an application to the LASSO and elastic net

ABSTRACT

The relaxed CQ algorithm is a very efficient algorithm for solving the split feasibility problem (SFP) whenever the convex subsets involved are level subsets of given convex functions. It approximates the original convex subset by a sequence of half-spaces that overcomes the difficulties for calculating the projection onto original convex subsets. In this paper, we propose a new inertial relaxed algorithm in which we approximate the original convex subset by a sequence of closed balls instead of half spaces. Moreover, we construct a new variable step-size that does not need any prior information of the norm. We then establish the weak convergence of the proposed algorithm under two different assumptions. Experimental results in the LASSO and elastic net methods show that our algorithm has a better performance than other relaxed algorithms.

Keywords:

• Split feasibility problem
• relaxed CQ algorithm
• variable step-size

2010 Mathematics Subject Classifications:

• 47J25
• 47J20
• 49N45
• 65J15

Acknowledgments

The authors would like to thank the referees for their very useful suggestions and comments, which greatly improve the manuscript. This work is supported by Natural Science Foundation of China (Grant No. 11971216) and Key Scientific Research Foundation of Universities in Henan Province (Grant No. 20A110029).

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by Natural Science Foundation of China (Grant No. 11971216) and Key Scientific Research Foundation of Universities in Henan Province (Grant No. 20A110029).