Convergence of Two Simple Methods for Solving Monotone Inclusion Problems in Reflexive Banach Spaces
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Publication:6402300
DOI10.1007/S00025-022-01694-5arXiv2206.08240MaRDI QIDQ6402300
Simeon Reich, Chinedu Izuchukwu, Y. Shehu
Publication date: 16 June 2022
Abstract: We propose two very simple methods, the first one with constant step sizes and the second one with self-adaptive step sizes, for finding a zero of the sum of two monotone operators in real reflexive Banach spaces. Our methods require only one evaluation of the single-valued operator at each iteration. Weak convergence results are obtained when the set-valued operator is maximal monotone and the single-valued operator is Lipschitz continuous, and strong convergence results are obtained when either one of these two operators is required, in addition, to be strongly monotone. We also obtain the rate of convergence of our proposed methods in real reflexive Banach spaces. Finally, we apply our results to solving generalized Nash equilibrium problems for gas markets.
Convex programming (90C25) Monotone operators and generalizations (47H05) Iterative procedures involving nonlinear operators (47J25) Numerical methods for variational inequalities and related problems (65K15) Variational and other types of inclusions (47J22)
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