11 papers
Difference-of-Convex Optimization via Inexact Smoothing Descent Methods: Difference of High-Order Moreau Envelopes
Alireza Kabgani, Moslem Zamani, Masoud Ahookhosh
This paper studies difference-of-convex (DC) optimization problems through smoothing descent techniques. In particular, we introduce the difference of high-order Moreau envelopes (…
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…
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-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…
Speeding Up Nonsmooth Bayesian MCMC Sampling via Inexact Proximal Unadjusted Langevin Algorithm
Susan Ghaderi, Alireza Kabgani, Yves Moreau +1
We study sampling from posterior distributions with nonsmooth composite potentials, a setting in which proximal-based Langevin methods are theoretically appealing but in practice l…
Robust Learning Meets Quasar-Convex Optimization: Inexact High-Order Proximal-Point Methods
Alireza Kabgani, Felipe Lara, Masoud Ahookhosh
Robust learning aims to maintain model performance under noise, corruption, and distributional shifts, which are prevalent in modern machine learning applications. This work shows…