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math.OC2026
Convergence and Stability of a Catching-Up Algorithm for Differential Inclusions with Maximal Monotone Operators
Tan H. Cao, Hassan Saoud
We study a catching-up algorithm for a class of differential inclusions driven by maximal monotone operators with continuous perturbations. Using a decomposition of the monotone op…
math.OC2025
Composite Lyapunov Criteria for Stability and Convergence with Applications to Optimization Dynamics
Hassan Saoud
We propose a composite Lyapunov framework for nonlinear autonomous systems that ensures strict decay through a pair of differential inequalities. The approach yields integral estim…
math.OC2025
Geometric Stability Analysis for Differential Inclusions Governed by Maximally Monotone Operators
Hassan Saoud, Michel Théra, Minh N. Dao
This paper develops a geometric framework for the stability analysis of differential inclusions governed by maximally monotone operators. A key structural decomposition expresses t…