A modified Liu-Storey scheme for nonlinear systems with an application to image recovery

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 15 اردیبهشت 1401  

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2022.75413.1107

نویسندگان

Aliyu Ibrahim Kiri¹؛ mohammed Yusuf Waziri ²؛ Kabiru Ahmed ²

¹Department of mathematical sciences, Bayero university, Kano

²Numerical Optimization Research Group, Bayero University, Kano, Nigeria

چکیده

Like the Polak-Ribi `ere-Polyak (PRP) and Hestenes-Stiefel (HS) methods, the classical Liu-Storey (LS) conjugate gradient scheme is widely believed to perform well numerically. This is attributed to the in-built capability of the method to conduct a restart when a bad direction is encountered. However, the scheme’s inability to generate descent search directions, which is vital for global convergence, represents its major shortfall. In this article, we present an LS-type scheme for solving system of monotone nonlinear equations with convex constraint. The scheme is based on the approach by Wang et al. (2020) and the projection scheme by Solodov and Svaiter (1998). The new scheme satisfies the important condition for global convergence and is suitable for non-smooth nonlinear problems. Furthermore, we demonstrate the method’s application in restoring blurry images in compressed sensing. The scheme’s global convergence is established under mild assumptions and preliminary numerical results show that the proposed method is promising and performs better than two recent methods in the literature.

کلیدواژه‌ها

Nonlinear Monotone Equations؛ Line search؛ Projection method؛ Signal processing؛ Convex constraint؛ Image de-blurring