6 papers · 1 filter
(Adaptive) Scaled gradient methods beyond locally Holder smoothness: Lyapunov analysis, convergence rate and complexity
Susan Ghaderi, Morteza Rahimi, Yves Moreau +1
This paper addresses the unconstrained minimization of smooth convex functions whose gradients are locally Holder continuous. Building on these results, we analyze the Scaled Gradi…
On fundamental properties of high-order forward-backward envelope
Alireza Kabgani, Masoud Ahookhosh
This paper studies the fundamental properties of the high-order forward-backward splitting mapping (HiFBS) and its associated high-order forward-backward envelope (HiFBE) through t…
Minimizing Smooth Kurdyka-Łojasiewicz Functions via Generalized Descent Methods: Convergence Rate and Complexity
Masoud Ahookhosh, Susan Ghaderi, Alireza Kabgani +1
This paper introduces a generalized descent algorithm (DEAL) for minimizing smooth nonconvex functions. If the objective function is nonsmooth, a smoothing technique (e.g., forward…
Inexact Levenberg-Marquardt methods under Hölder metric subregularity
Bas Symoens, Morteza Rahimi, Masoud Ahookhosh
This paper investigates two inexact Levenberg-Marquardt (LM) methods for solving systems of nonlinear equations. Both approaches compute approximate search directions by solving th…
Second-order methods for provably escaping strict saddle points in composite nonconvex and nonsmooth optimization
Alexander Bodard, Masoud Ahookhosh, Panagiotis Patrinos
This study introduces two second-order methods designed to provably avoid saddle points in composite nonconvex optimization problems: (i) a nonsmooth trust-region method and (ii) a…
Projected subgradient methods for paraconvex optimization: Application to robust low-rank matrix recovery
Morteza Rahimi, Susan Ghaderi, Yves Moreau +1
This paper is devoted to the class of paraconvex functions and presents some of its fundamental properties, characterization, and examples that can be used for their recognition an…