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 three distinct parts:
Qualitative Research: optimality conditions for nonsmooth optimization problems, properties of generalized convexity and monotonicity, stability, regularity, etc.
Quantitative Research: generalized first- and second-order numerical methods for solving nonsmooth nonconvex optimization problems including unconstrained optimization problems, constrained optimization problems, composite optimization problems, etc.
Applications: applying results in qualitative and quantitative studies for real practical optimization models in other fields such as machine learning, economics, statistics, etc.
I am a PI/co-PI of the following grants:
National Science Foundation, Grant No. DMS-2526465, "Conference: 2025 Midwest Optimization Meeting”; October 01, 2025 - September 30, 2026 (Co-Principal Investigator)
The following grants provided support for my research and travel:
US National Science Foundation, Grant No. DMS-2534607, “Conference: SIAM Great Lakes 2025 Meeting”.
US National Science Foundation, Grant No. DMS-2204519, “Variational Analysis: Theory, Algorithms, and Applications”.
US National Science Foundation, Grant No. DMS-2323340, “Conference: 2023 Midwest Optimization Meeting”.
US National Science Foundation, Grant No. DMS-1808978, “Advanced Research on Second-Order Variational Analysis with New Applications to Optimization, Control, and Practical Modeling”.
US National Science Foundation, Grant No. DMS-1512846, “Second-Order Variational Analysis and Its Applications”.
US Air Force Office of Scientific Research, Grant No. 15RT0462.
(with P. D. Khanh, B. S. Mordukhovich and L. D. Viet) Generalized Twice Differentiability and Quadratic Bundles in Second-Order Variational Analysis, to appear in Set-Valued and Variational Analysis, (2025) arxiv
(with P. D. Khanh, B. S. Mordukhovich and L. D. Viet) Characterizations of Strong Variational Convexity and Tilt Stability via Quadratic Bundles, to appear in Journal of Convex Analysis, (2025) arxiv
(with P. D. Khanh, V. V. H. Khoa and L. D. Viet) Lipschitz Modulus of Convex Functions via Functions Values, Optimization Letters, https://doi.org/10.1007/s11590-025-02218-0 (2025) 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, https://doi.org/10.1007/s10013-025-00739-w (2025) 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, https://doi.org/10.1287/moor.2023.0270 (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
(with P. D. Khanh and B. S. Mordukhovich) Coderivative-Based Newton Methods in Structured Nonconvex and Nonsmooth Optimization, 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
Optimization
Set-Valued and Variational Analysis
SIAM Journal on Optimization
Here is my ORCID ID profile: https://orcid.org/0000-0003-1211-8025.