My main research areas are nonsmooth optimization and variational analysis. I am interested in both theoretical and numerical aspects with practical applications. To provide further clarity, my research projects can be categorized into two main distinct parts:
Qualitative Research:
Optimality conditions for nonsmooth and nonconvex optimization problems
Optimality conditions for optimal control problems
Characterizations of generalized convexity of functions and applications to optimization and optimal control problems
Local and global maximal monotonicity, generalized monotonicity of set-valued operators and applications to variational inequality problems
Well-posedness, stability and sensitivity analysis of dynamical systems
Quantitative Research:
First- and second-order numerical methods for solving nonsmooth and nonconvex optimization problems
Numerical methods for variational inequality problems
Numerical methods for dynamical systems, optimal control problems
Numerical methods for solving practical models in machine learning, statistics, engineering, economics, etc.
I am a PI/co-PI of the following grants:
Early Career Scholars Program (ECSP) to Advance Multi-Disciplinary Research Teams - University of North Dakota under Project 43700-2375-UND0031286, "Variational-Analysis-Based Numerical Methods for Difference Programming and Applications in Wireless Systems"; January 05, 2026 - December 31, 2026 (Principal Investigator).
US National Science Foundation, Grant No. DMS-2526465, "Conference: 2025 Midwest Optimization Meeting”; October 01, 2025 - September 30, 2026 (Co-Principal Investigator).
(with P. D. Khanh and B. S. Mordukhovich) Coderivative-based Newton methods in structured nonconvex and nonsmooth optimization, to appear in Mathematical Programming, (2026) arxiv
(with P. D. Khanh, B. S. Mordukhovich and L. D. Viet) Characterizations of strong variational convexity and tilt stability via quadratic bundles, Journal of Convex Analysis, 33, 903-924 (2026) arxiv Journal
(with P. D. Khanh, B. S. Mordukhovich and L. D. Viet) Generalized twice differentiability and quadratic bundles in second-order variational analysis, Set-Valued and Variational Analysis, 34 (2026) arxiv Journal
(with P. D. Khanh, V. V. H. Khoa and B. S. Mordukhovich) Local maximal monotonicity in variational analysis and optimization, Mathematics of Operations Research, 51(2), 938-955 (2026) arxiv Journal
(with P. D. Khanh, V. V. H. Khoa and L. D. Viet) Lipschitz modulus of convex functions via functions values, Optimization Letters, 20, 197–212 (2026) arxiv Journal
(with P. D. Khanh, V. V. H. Khoa and B. S. Mordukhovich) Local minimizers of nonconvex functions in Banach spaces via Moreau envelopes, Vietnam Journal of Mathematics, 53, 803–813 (2025) arxiv Journal
(with P. D. Khanh, V. V. H. Khoa and B. S. Mordukhovich) Second-order subdifferential optimality conditions in nonsmooth optimization, SIAM Journal on Optimization, 35(2), 678-711 (2025) arxiv Journal
(with P. D. Khanh, B. S. Mordukhovich and D. B. Tran) Inexact proximal methods for weakly convex functions, Journal of Global Optimization, 91(3), 611-646 (2025) arxiv, Journal
(with P. D. Khanh, V. V. H. Khoa and B. S. Mordukhovich) Variational and strong variational convexity in infinite-dimensional variational analysis, SIAM Journal on Optimization, 34(3), 2756-2787 (2024) arxiv, Journal
(with P. D. Khanh, B. S. Mordukhovich and D. B. Tran) Globally convergent coderivative-based generalized Newton methods in nonsmooth optimization. Mathematical Programming, 205(1), 373-429 (2024) arxiv, Journal
(with P. D. Khanh and B. S. Mordukhovich) Variational convexity of functions and variational sufficiency in optimization, SIAM Journal on Optimization, 33(2), 1121-1158 (2023) arxiv, Journal
(with P. D. Khanh and B. S. Mordukhovich) A generalized Newton method for subgradient systems. Mathematics of Operations Research, 48(4), 1811-1845 (2023) arxiv, Journal
(with P. D. Khanh, B. S. Mordukhovich and D. B. Tran) Generalized damped Newton algorithms in nonsmooth optimization via second-order subdifferentials. Journal of Global Optimization, 86(1), 93-122 (2023) arxiv, Journal
(with P. D. Khanh) Second-order characterizations of quasiconvexity and pseudoconvexity for differentiable functions with Lipschitzian derivatives. Optimization Letters, 14(8), 2413-2427 (2020) PDF, Journal
(with P. D. Khanh) Second-order characterizations of C1-smooth robustly quasiconvex functions. Operations Research Letters, 46(6), 568-572 (2018) PDF, Journal
New characterizations of nonsmooth convex functions via generalized derivatives (2026) arxiv
(with J. Chen and S. Zeng) A coupled nonsmooth dynamical system: global well-posedness, stability and sensitivity analysis (2026) arxiv
(with T. Tran) New globalized Newton-type methods for nonconvex optimization problems, submitted (2026) arxiv
Generalized Coderivative-Based Newtonian Methods In Nonsmooth Nonconvex Optimization And Applications (2024), Wayne State University Dissertations, PDF
(with P. D. Khanh, V. V. H. Khoa and B. S. Mordukhovich) Variational convexity of functions in Banach spaces, Functional Analysis and Continuous Optimization (J. M. Amigo et al., eds), Springer Proceedings in Mathematics and Statistics (M.J. Canovas et al., eds), 424, pp. 237–260, https://doi.org/10.1007/978-3-031-30014-1_11, Springer (2023) arxiv, Book Chapter
I am a referee for journals including:
Applied Mathematics and Optimization
Journal of Optimization Theory and Applications
Journal of Global Optimization
Mathematics of Operations Research
Mathematical Programming
Nonlinear Analysis: Hybrid Systems
Optimization
Set-Valued and Variational Analysis
SIAM Journal on Optimization
Here is my ORCID ID profile: https://orcid.org/0000-0003-1211-8025.