8 papers
Reducing the Lipschitz Constant in Tseng Algorithm and the Convergence Analysis
Ba Khiet Le, Minh Thuan Tran, Thi Thanh Tien Pham +1
In this paper, we prove the weak and linear convergence of Tseng algorithm applied to the zero of sum of two operators problem where each operator is not necessarily monotone while…
Splitting Algorithms Using Pairs Monotonicity to Solve the Sum of Two Non-monotone Operators Problem
Ba Khiet Le, Zakaria Mazgouri, Michel Théra
This paper is concerned with solving the problem of finding a zero of the sum of a single-valued operator and a set-valued operator, neither of which is assumed to be monotone, in…
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…
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…
Compact R-Continuity with Applications to Solving Inclusions and Convergence of Algorithms
Ba Khiet Le, Boris S. Mordukhovich, Michel A. Thera
This paper investigates the notion of compact R-continuity and its specifications for set-valued mappings between Banach spaces. We reveal several important properties of compact R…
Solving Non-Monotone Inclusions Using Monotonicity of Pairs of Operators
Ba Khiet Le, Minh N. Dao, Michel Théra
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 tran…
Explicit Convergence Rate of The Proximal Point Algorithm under R-Continuity
Ba Khiet Le, Michel Théra
The paper provides a thorough comparison between R-continuity and other fundamental tools in optimization such as metric regularity, metric subregularity and calmness. We show that…
R-Continuity with Applications to Convergence Analysis of Tikhonov Regularization and DC Programming
Ba Khiet Le
In the paper, we study the convergence analysis of Tikhonov regularization in finding a zero of a maximal monotone operator using the notion of R-continuity. Applications to convex…