5 papers
Convergence and Stability Analysis of a Generalized Proximal Point Algorithm and Its Inexact Version
Ba Khiet Le, Boris S. Mordukhovich, Michel A. Thera
In this paper, we introduce the notion of adaptive strong monotonicity and establish a linear convergence of the recently proposed Generalized Proximal Point Algorithm (GPPA) for c…
Inexact Proximal Point and Tseng Algorithms with Nonsummable Errors to Solve Monotone Inclusions
Ba Khiet Le, Boris S. Mordukhovich, Michel A. Thera
In this paper, we establish, for the first time in the literature, the convergence of the practical versions of the Inexact Proximal Point Algorithm (IPPA) and the Inexact Tseng Al…
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…
Monotonicity of Pairs of Operators and Generalized Inertial Proximal Method
Ba Khiet Le, Zakaria Mazgouri, Michel Théra
Monotonicity of pairs of operators is an extension of monotonicity of operators, which plays an important role in solving non-monotone inclusions. One of challenging problems in th…
Weak and strong convergence of a relaxed inertial proximal splitting algorithm for solving hierarchical equilibrium problems
Zakaria Mazgouri, Hassan Riahi, Michel Théra
In this chapter, we introduce the relaxed inertial proximal splitting algorithm (RIPSA) for hierarchical equilibrium problems. Using Opial-Passty's lemma, we first establish weak e…