Solving Non-Monotone Inclusions Using Monotonicity of Pairs of Operators

Ba Khiet Le (), Minh N. Dao () and Michel A. Théra ()
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Ba Khiet Le: Faculty of Mathematics and Statistics, Ton Duc Thang University
Minh N. Dao: RMIT University
Michel A. Théra: XLIM UMR-CNRS 7252, Université de Limoges

Journal of Optimization Theory and Applications, 2025, vol. 207, issue 1, No 18, 19 pages

Abstract: Abstract In this paper, under the monotonicity of pairs of operators, we propose some generalized proximal point algorithms to solve non-monotone inclusions using warped and transformed resolvents. We establish weak, strong, and linear convergence of the proposed algorithms under mild conditions.

Keywords: Non-monotone inclusions; Monotonicity of pairs of operators; Nonconvex programming; Warped resolvents; Transformed resolvents; Proximal point algorithm; 49J52; 49J53 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02770-w

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