Forward-Backward-Forward Dynamical Systems and A Generalized Bregman-Type Algorithm for Quasimonotone Variational Inequalities

A Two-Step Inertial Bregman-Tseng Method for Non-Monotone Variational Inequality Problems in Reflexive Banach Spaces

In this paper, we introduce a novel two-step inertial Bregman--Tseng algorithm for solving non-monotone variational inequality problems in reflexive Banach spaces. The proposed method combines a two-step inertial extrapolation scheme with a Bregman forward-backward-forward (Tseng-type) framework, leading to a computati...

Finite-time and predefined-time dynamical systems for solving strongly pseudomonotone mixed equilibrium problems

This paper establishes the existence and uniqueness of the equilibrium solution, proves the global exponential stability of the associated continuous-time nominal system, and constructs an FT stable PDS whose equilibrium point coincides with the solution of the MEP and derive sufficient conditions for finite-time conve...

A modified fast Popov’s method for pseudo-monotone variational inequalities

Nonlinear Forward-Backward Algorithm for Solving Non-monotone+Lipschitz Inclusions with Applications to Adjoint Mismatch Problems

This article presents a novel algorithmic framework for solving a broad class of nonlinear inclusion problems involving non-monotone and Lipschitz continuous operators. Our primary motivation originates from the study of adjoint mismatch problems, which frequently arise in inverse problems and data science when the adj...

Forward-Backward McKean-Vlasov System with Jumps and a Monotone Source With \`a Control-Shifted Interface : Well-Posedness, Stability, and Yosida Rates

We study a forward-backward McKean-Vlasov system with jumps and one-way coupling: the forward equation is independent of the backward variables, whereas the BSDE depends on the forward state and its law. A source generated by a maximal monotone operator is evaluated along the forward state and then accumulated in the b...

Approximation of Bi-Continuous Semigroups in the Trotter-Kato Framework: Application to Diffusion Equations with Non-Local Boundary Conditions

This study develops and practically reformulates the Trotter–Kato theorem for the approximation of bi-continuous semigroups defined on Banach spaces with weaker locally convex Hausdorff topologies. This method extends the Trotter–Kato framework to semigroups with weak continuity by moving the analysis from the classica...