Research Interests

My main research areas are nonsmooth optimization and variational analysis. I am interested in both theoretical and numerical aspects with applications in machine learning and statistics. 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, difference programming, bilevel optimization, stochastic optimization, etc.

Applications: applying aforementioned results in qualitative and quantitative studies for real practical optimization problems such as LASSO, fast best subsets selection, support vector machine, quadratic programming, clustering problems, minimax problems, etc. 

Peer-Reviewed Publications

1. (with P. D. Khanh, V. V. H. Khoa and B. S. Mordukhovich) Local Minimizers of Nonconvex Functions in Banach Spaces via Moreau Envelopes, to appear in Vietnam Journal of Mathematics, (2024) arxiv (Scopus, ESCI, Q2)

2. (with P. D. Khanh, V. V. H. Khoa and B. S. Mordukhovich) Local maximal monotonicity in variational analysis and optimization, to appear in Mathematics of Operations Research, (2024) arxiv (SCIE, Q1)

3. (with P. D. Khanh, B. S. Mordukhovich and D. B. Tran) Inexact proximal methods for weakly convex functions, to appear in Journal of Global Optimization, (2024) arxiv (SCIE, Q2)

4. (with P. D. Khanh, V. V. H. Khoa and B. S. Mordukhovich) Variational and Strong Variational Convexity in Infinite-Dimensional Variational Analysis, to appear in SIAM Journal on Optimization, (2024) arxiv (SCIE, Q1)

5. (with P. D. Khanh, B. S. Mordukhovich and D. B. Tran) Globally Convergent Coderivative-Based Generalized Newton Methods in Nonsmooth Optimization. Mathematical Programming, 205, 373-429 (2024) arxiv, Journal (SCIE, Q1)

6. (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 (SCIE, Q1)

7. (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 (SCIE, Q1)

8. (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 (SCIE, Q1)

9. (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 (SCIE, Q1)

10. (with P. D. Khanh) Second-order characterizations of C1-smooth robustly quasiconvex functions. Operations Research Letters, 46(6), 568-572 (2018) PDF, Journal (SCIE, Q2)

Book Chapters 

1. (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

Submitted Manuscripts 

1. (with P. D. Khanh, V. V. H. Khoa and L. D. Viet) Lipschitz Modulus of Convex Functions via Functions Values, submitted. 

2. (with P. D. Khanh and B. S. Mordukhovich) Coderivative-Based Newton Methods in Structured Nonconvex and Nonsmooth Optimization, arxiv

3. (with P. D. Khanh, V. V. H. Khoa and B. S. Mordukhovich) Second-Order Subdifferential Optimality Conditions in Nonsmooth Optimization, second review round in SIAM Journal on Optimization, arxiv

Thesis and Dissertation

1. Bachelor Thesis (written in Vietnamese): Second-order Subdifferentials and Applications. PDF 

2. Doctoral Dissertation: Generalized Coderivative-Based Newtonian Methods in Nonsmooth Nonconvex Optimization and Applications. PDF 

Referee Service

I am a referee for journals including:

• Applied Mathematics and Optimization

• Journal of Optimization Theory and Applications

• Journal of Global Optimization

• Optimization

• Set-Valued and Variational Analysis

• SIAM Journal on Optimization 

Here is my ORCID ID profile: https://orcid.org/0000-0003-1211-8025.

Memberships

• International Working Group on Generalized Convexity

• Society for Industrial and Applied Mathematics (SIAM)

• Group of Analysis and Applied Mathematics (GAAM), Department of Mathematics, Ho Chi Minh City University of Education, Ho Chi Minh City, Vietnam