A Perry-type derivative-free algorithm for solving nonlinear system of equations and minimizing ℓ1 regularized problem. (3rd June 2021)

• Record Type: Journal Article
• Authors: Awwal, A. M.; Kumam, Poom; Mohammad, Hassan; Watthayu, Wiboonsak; Abubakar, A. B.
• Is Part Of: Optimization. Volume 70:Number 5/6(2021)
• Page Start: 1231
• Page End: 1259
• Publication Date: 2021-06-03
• Subjects: Derivative-free method -- nonlinear equations -- projection method -- signal recovery; 90C30 -- 90C06 -- 90C56; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1808647
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we propose a Perry-type derivative-free algorithm for solving systems of nonlinear equations. The algorithm is based on the well-known BFGS quasi-Newton method with a modified Perry's parameter. The global convergence of the algorithm is established without assumption on the regularity or boundedness of the solution set. Meanwhile, the sequence of iterates generated by the algorithm converges globally to the solution of the problem provided that the function is Lipschitz continuous and monotone. Preliminary numerical experiments on some collection of general nonlinear equations and convex constrained nonlinear monotone equations demonstrate the efficiency of the algorithm. Moreover, we successfully apply the proposed algorithm to solve signal recovery problem.