1 citations · 2 across the 9 of their papers we have counts for
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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…
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…
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…
General Derivative-Free Optimization Methods under Global and Local Lipschitz Continuity of Gradients
Pham Duy Khanh, Boris S. Mordukhovich, Dat Ba Tran
This paper addresses the study of derivative-free smooth optimization problems, where the gradient information on the objective function is unavailable. Two novel general derivativ…
Inexact proximal methods for weakly convex functions
Pham Duy Khanh, Boris Mordukhovich, Vo Thanh Phat +1
This paper proposes and develops inexact proximal methods for finding stationary points of the sum of a smooth function and a nonsmooth weakly convex one, where an error is present…
A New Inexact Gradient Descent Method with Applications to Nonsmooth Convex Optimization
Pham Duy Khanh, Boris S. Mordukhovich, Dat Ba Tran
The paper proposes and develops a novel inexact gradient method (IGD) for minimizing C1-smooth functions with Lipschitzian gradients, i.e., for problems of C1,1 optimization. We sh…
Inexact reduced gradient methods in nonconvex optimization
Pham Duy Khanh, Boris S. Mordukhovich, Dat Ba Tran
This paper proposes and develops new linesearch methods with inexact gradient information for finding stationary points of nonconvex continuously differentiable functions on finite…
Globally Convergent Coderivative-Based Generalized Newton Methods in Nonsmooth Optimization
Pham Duy Khanh, Boris Mordukhovich, Vo Thanh Phat +1
This paper proposes and justifies two globally convergent Newton-type methods to solve unconstrained and constrained problems of nonsmooth optimization by using tools of variationa…
Generalized Damped Newton Algorithms in Nonsmooth Optimization via Second-Order Subdifferentials
Pham Duy Khanh, Boris Mordukhovich, Vo Thanh Phat +1
The paper proposes and develops new globally convergent algorithms of the generalized damped Newton type for solving important classes of nonsmooth optimization problems. These alg…