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math.OC2026
Inexact DC Algorithms in Hilbert Spaces with Applications to PDE-Constrained Optimization
P. D. Khanh, V. V. H. Khoa, B. S. Mordukhovich +2
In this paper, we design and apply novel inexact adaptive algorithms to deal with minimizing difference-of-convex (DC) functions in Hilbert spaces. We first introduce I-ADCA, an in…
math.OC2025
Convergence of First-Order Algorithms with Momentum from the Perspective of an Inexact Gradient Descent Method
Pham Duy Khanh, Boris Mordukhovich, Dat Ba Tran
This paper introduces a novel inexact gradient descent method with momentum (IGDm) considered as a general framework for various first-order methods with momentum. This includes, i…
math.OC2024
Fundamental Convergence Analysis of Sharpness-Aware Minimization
Pham Duy Khanh, Hoang-Chau Luong, Boris S. Mordukhovich +1
The paper investigates the fundamental convergence properties of Sharpness-Aware Minimization (SAM), a recently proposed gradient-based optimization method [Foret et al., 2021] tha…