6 papers · 1 filter
Isolated calmness of regularized linear inverse problems
Tran T. A. Nghia, Huy N. Pham, Nghia V. Vo +1
This paper studies the isolated calmness property of solution mappings arising from convex regularized linear inverse problems. We mainly establish a tangent-cone characterization…
Nonsmooth Newton methods with effective subspaces for polyhedral regularization
Tran T. A. Nghia, Nghia V. Vo, Khoa V. H. Vu
We propose several new nonsmooth Newton methods for solving convex composite optimization problems with polyhedral regularizers, while avoiding the computation of complicated secon…
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…
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…