A Novel Forward-Backward Algorithm for Solving Convex Minimization Problem in Hilbert Spaces

Suthep Suantai, Kunrada Kankam and Prasit Cholamjiak
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Suthep Suantai: Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
Kunrada Kankam: School of Science, University of Phayao, Phayao 56000, Thailand
Prasit Cholamjiak: School of Science, University of Phayao, Phayao 56000, Thailand

Mathematics, 2020, vol. 8, issue 1, 1-13

Abstract: In this work, we aim to investigate the convex minimization problem of the sum of two objective functions. This optimization problem includes, in particular, image reconstruction and signal recovery. We then propose a new modified forward-backward splitting method without the assumption of the Lipschitz continuity of the gradient of functions by using the line search procedures. It is shown that the sequence generated by the proposed algorithm weakly converges to minimizers of the sum of two convex functions. We also provide some applications of the proposed method to compressed sensing in the frequency domain. The numerical reports show that our method has a better convergence behavior than other methods in terms of the number of iterations and CPU time. Moreover, the numerical results of the comparative analysis are also discussed to show the optimal choice of parameters in the line search.

Keywords: convex minimization problem; forward-backward splitting method; Hilbert space; line search (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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