1 citations · 3 across the 14 of their papers we have counts for
16 papers
A Coupled Nonsmooth Dynamical System: Global Well-Posedness, Stability and Sensitivity Analysis
Shengda Zeng, Jia Chen, Vo Thanh Phat
This paper studies a coupled nonsmooth dynamical system in which a semilinear evolution equation is coupled with an implicit algebraic law governed by the normal cone to a time-dep…
New Globalized Newton-Type Methods for Nonconvex Optimization Problems
Vo Thanh Phat, Tuyen Tran
Newton's method is one of the most effective second-order algorithms for smooth optimization because of its fast local convergence. However, existing globally convergent Newton-typ…
New Characterizations of Nonsmooth Convex Functions via Generalized Derivatives
Vo Thanh Phat
This paper studies the convexity properties of nonsmooth extended-real-valued weakly convex functions, a class of functions that is central to modern optimization and its applicati…
Characterizations of Variational Convexity and Tilt Stability via Quadratic Bundles
Pham Duy Khanh, Boris S. Mordukhovich, Vo Thanh Phat +1
In this paper, we establish characterizations of variational -convexity and tilt stability for prox-regular functions in the absence of subdifferential continuity via quadratic…
Lipschitz Modulus of Convex Functions via Function Values
Pham Duy Khanh, Vu Vinh Huy Khoa, Vo Thanh Phat +1
In this note, we establish the Lipschitz continuity of finite-dimensional globally convex functions on all given balls and global Lipschitz continuity for eligible functions of tha…
Coderivative-Based Newton Methods in Structured Nonconvex and Nonsmooth Optimization
Pham Duy Khanh, Boris S. Mordukhovich, Vo Thanh Phat
This paper proposes and develops new Newton-type methods to solve structured nonconvex and nonsmooth optimization problems with justifying their fast local and global convergence b…
Second-Order Subdifferential Optimality Conditions in Nonsmooth Optimization
Pham Duy Khanh, Vu Vinh Huy Khoa, Boris S. Mordukhovich +1
The paper is devoted to deriving novel second-order necessary and sufficient optimality conditions for local minimizers in rather general classes of nonsmooth unconstrained and con…
Local Minimizers of Nonconvex Functions in Banach Spaces via Moreau Envelopes
Pham Duy Khanh, Vu Vinh Huy Khoa, Boris S. Mordukhovich +1
This paper investigates the preservation of local minimizers and strong minimizers of extended-real-valued lower semicontinuous functions under taking their Moreau envelopes. We ad…
Variational and Strong Variational Convexity in Infinite-Dimensional Variational Analysis
Pham Duy Khanh, Vu Vinh Huy Khoa, Boris S. Mordukhovich +1
This paper is devoted to a systematic study and characterizations of the fundamental notions of variational and strong variational convexity for lower semicontinuous functions. Whi…
Local Maximal Monotonicity in Variational Analysis and Optimization
Pham Duy Khanh, Vu Vinh Huy Khoa, Boris S. Mordukhovich +1
The paper is devoted to a systematic study and characterizations of notions of local maximal monotonicity and their strong counterparts for set-valued operators that appear in vari…
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…
Variational Convexity of Functions in Banach Spaces
Pham Duy Khanh, Vu Vinh Huy Khoa, Boris S. Mordukhovich +1
This paper addresses the study and characterizations of variational convexity of extended-real-valued functions on Banach spaces. This notion has been recently introduced by Rockaf…
Variational Convexity of Functions and Variational Sufficiency in Optimization
Pham Duy Khanh, Boris S. Mordukhovich, Vo Thanh Phat
The paper is devoted to the study, characterizations, and applications of variational convexity of functions, the property that has been recently introduced by Rockafellar together…
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…
A Generalized Newton Method for Subgradient Systems
Pham Duy Khanh, Boris Mordukhovich, Vo Thanh Phat
This paper proposes and develops a new Newton-type algorithm to solve subdifferential inclusions defined by subgradients of extended-real-valued prox-regular functions. The propose…