5 papers
Relative Weak Convexity and Projected Subgradient Methods: Analysis and Convergence
Morteza Rahimi, Masoud Ahookhosh
We introduce the class of relatively weakly convex functions, which extends the classical notion of weak convexity by measuring nonconvexity relative to a distance-generating funct…
Minimizing Smooth Kurdyka-Åojasiewicz 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…
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…
(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…
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…