Solving Non-Monotone Inclusions Using Monotonicity of Pairs of Operators

2025/01/23 by Ba Khiet Le, Le, Ba Khiet, Minh N. Dao +4 · 2 citations
Computer Science · Engineering · Mathematics · #Aerospace Engineering and Control Systems #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2501.13637

openalex publication_date 2025/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 resolvents and transformed resolvents. The weak, strong, and linear convergence of the proposed algorithms are established under very mild conditions.

Citations

• State-Dependent Sweeping Processes: Asymptotic Behavior and Algorithmic Approaches

Cited by

• Scaled relative graphs for pairs of operators beyond classical monotonicity
• Compact R-Continuity with Applications to Solving Inclusions and Convergence of Algorithms

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