Journal
SYMMETRY-BASEL
Volume 12, Issue 6, Pages -Publisher
MDPI
DOI: 10.3390/sym12060874
Keywords
spectral gradient method; nonlinear monotone equations; projection method; line search; image deblurring
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Funding
- Petchra Pra Jom Klao Doctoral Scholarship for Ph.D. program of King Mongkut's University of Technology Thonburi (KMUTT)
- Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT
- Petchra Pra Jom Klao Ph.D. Research Scholarship from King Mongkut's University of Technology Thonburi [42/2560]
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In this paper, we propose a two-step iterative algorithm based on projection technique for solving system of monotone nonlinear equations with convex constraints. The proposed two-step algorithm uses two search directions which are defined using the well-known Barzilai and Borwein (BB) spectral parameters.The BB spectral parameters can be viewed as the approximations of Jacobians with scalar multiple of identity matrices. If the Jacobians are close to symmetric matrices with clustered eigenvalues then the BB parameters are expected to behave nicely. We present a new line search technique for generating the separating hyperplane projection step of Solodov and Svaiter (1998) that generalizes the one used in most of the existing literature. We establish the convergence result of the algorithm under some suitable assumptions. Preliminary numerical experiments demonstrate the efficiency and computational advantage of the algorithm over some existing algorithms designed for solving similar problems. Finally, we apply the proposed algorithm to solve image deblurring problem.
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