7 papers
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…
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 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…
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…
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…
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…