Locating Theorems of Differential Inclusions Governed by Maximally Monotone Operators
Minh Ngoc Dao, Hassan Saoud, Michel A. Théra · SIAM Journal on Optimization · 2023
Abstract. In this paper, we are interested in studying the asymptotic behavior of the solutions of differential inclusions governed by maximally monotone operators. In the case where the LaSalle’s invariance principle is inconclusive, we provide a refined version of the invariance principle theorem. This result derives from the problem of locating the [Formula: see text]-limit set of a bounded solution of the dynamic. In addition, we propose an extension of LaSalle’s invariance principle, which allows us to give a sharper location of the [Formula: see text]-limit set. The provided results are given in terms of nonsmooth Lyapunov pair-type functions.