Author

Samir Adly

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Open access 2018

Newton-Type Method for Solving Generalized Equations on Riemannian Manifolds

This paper is devoted to the study of Newton-type algorithm for solving inclusions involving set-valued maps defined on Riemannian manifolds. We provide some sufficient conditions ensuring the existence as well as the quadratic convergence of Newton sequence. The material studied in this paper is based on Riemannian ge...

Samir Adly, Ngai van Huynh, V. Nguyen · Journal of Convex Analysis · 1 citation

Open access 2018

Quasi-Newton Methods for Solving Nonsmooth Equations: Generalized Dennis-Moré Theorem and Broyden's Update

We study the quasi-Newton method by using set-valued approximations for solving generalized equations without smoothness assumptions. The set-valued approximations appear naturally when dealing with nonsmooth problems, or even in smooth cases, data in almost concrete applications are not exact. We present a generalizat...

Samir Adly, Ngai van Huynh · Journal of Convex Analysis · 6 citations

Open access 2022

Dennis-Moré Condition for Set-Valued Vector Fields and the Superlinear Convergence of Broyden Updates in Riemannian Manifolds

This paper deals with the quasi-Newton type scheme for solving generalized equations involving set-valued vector fields on Riemannian manifolds. We establish some conditions ensuring the superlinear convergence for the iterative sequence which approximates a solution of the generalized equations. Such conditions can be...

Samir Adly, Ngai van Huynh, V. V. Nguyen · Journal of Convex Analysis · 0 citations

Preprint Aug 2026

Stationarity Floors and Vanishing Perturbations in Sharpness-Aware Minimization

We study a deterministic family of sharpness-aware minimization methods for smooth nonconvex functions. The perturbation is $$ y_k=x_k+\rho\, \frac{\nabla f(x_k)}{\norm{\nabla f(x_k)}^\alpha}, \qquad 0\leq\alpha\leq 1, $$ so that its effective radius is $\rho\norm{\nabla f(x_k)}^{1-\alpha}$. For $0<\alpha\leq1$, we giv...

Samir Adly, B. K. Le · 0 citations