6 papers
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…
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…
An inertial proximal splitting algorithm for hierarchical bilevel equilibria in Hilbert spaces
Aicha Balhag, Zakaria Mazgouri, Hassan Riahi +1
In this article, we aim to approximate a solution to the bilevel equilibrium problem for short: find such that $ g(\bar{x}, y) \geq 0, \…
On the stability of second order parametric ordinary differential equations and applications
Z. Mazgouri, A. El Ayoubi
This work deals with Lipschitz stability for a parametric version of the general second order Ordinary Differential Equation (ODE) initial-value Cauchy problem. We first establish…
Weak and strong convergence of an inertial proximal method for solving bilevel monotone equilibrium problems
AÏcha Balhag, Zakaria Mazgouri, Michel Théra
In this paper, we introduce an inertial proximal method for solving a bilevel problem involving two monotone equilibrium bifunctions in Hilbert spaces. Under suitable conditions an…