RESEARCH INTERESTS

Nonsmooth Optimization, Variational Analysis, Mathematical Programming, Compressive Sensing, Statistical Learning

GRANTS

• NSF Grant DMS-1816386, Collaborative research: Second-order variational analysis in structured optimization and algorithms with applications (lead PI, co-PI: J. Y. Bello-Cruz), Sep 2018-2021

• Oakland University, Faculty Research Fellowships, Tilt stability in sparse optimization with applications to signal processing (PI), May-August 2018 

• Oakland University, Faculty Research Fellowships, Full stability approach to augmented Lagrangian methods in nonlinear programming (PI), May-August 2015

PUBLICATIONS 

1. T. T. A. Nghia: Geometric characterizations of Lipschitz stability for convex optimization problems, 2024, arXiv:2402.05215, submitted. 

2. J. Fadili, T. T. A. Nghia, and D. N. Phan: Solution uniqueness of convex optimization problems via the radial cone, 2024, arXiv:2401.10346, submitted. 

3. J. Fadili, T. T. A. Nghia, and D. N. Phan: Geometric characterizations of strong minima with applications to nuclear norm minimization problems, 2023, arXiv:2308.09224 , submitted.

4. J. Fadili, T. T. A. Nghia, and T. T.T. Tran: Sharp, strong, and unique minimizers for low complexity robust recovery, IMA Information and Inference, 12 (3), 1461--1513, 2023. arXiv2111.05444

5. J. B. Bello-Cruz, G. Li, and T. T. A. Nghia: Quadratic growth condition and uniqueness of optimal solution to Lasso, J. Optim. Theory Appl., 194, 167–190, 2022. (This is Part II of the paper "On the Q-linear convergence of forward-backward splitting method. Part I: Convergence analysis" below)

6. N. H. Chieu, L. V. Hien, T. T. A. Nghia, and H. A. Tuan: Quadratic growth and strong metric subregularity of the subdifferential via subgradient graphical derivative, SIAM J. Optim., 31(1), 545–568, 2021.

7. J. B. Bello-Cruz, G. Li, and T. T. A. Nghia: On the Q-linear convergence of forward-backward splitting method. Part I: Convergence analysis,  J. Optim. Theory Appl., 188 , 378–401, 2021.

8. T. T. A. Nghia, D. T. Pham, and  T. T. T. Tran: On the positive definiteness of the limiting coderivative for set-valued mappings, Set-Valued and Var. Anal.,  29, 283–300, 2021. 

9. B. S. Mordukhovich, T. T. A. Nghia, and D. T. Pham: Full stability of general parametric variational systems, Set-Valued and Var. Anal. 26 , 911-946, 2018. arXiv 

10. N. H. Chieu, L. V. Hien, and T. T. A. Nghia: Characterization of tilt stability via subgradient graphical derivative with applications to nonlinear programming, SIAM J. Optim., 28, 2246-2273, 2018. arXiv

11. G. Li, B. S. Mordukhovich, T. T. A. Nghia, and T-S. Pham: Error bounds for parametric polynomial systems with applications to higher-order stability analysis and convergence rate, Math. Program., 168, 313-343, 2018. arXiv 

12. J. Y. Bello-Cruz and T. T. A. Nghia: On the convergence of the proximal forward-backward splitting method with linesearches, Optim. Method Softw., 31, 1209-1239, 2016. arXiv

13. H. H. Bauschke, J. Y. Bello-Cruz, T. T. A. Nghia, H. M. Phan, and X. Wang: Optimal rates of linear convergence of relaxed alternating projections and generalized Douglas-Rachford methods for two subspaces, Numer. Algorithms, 73, 33-76, 2016. pdf

14. B. S. Mordukhovich and T. T. A. Nghia: Local monotonicity and full stability for parametric variational systems, SIAM J. Optim., 23, 1032-1059, 2016. arXiv

15. N. H. Chieu, G.M. Lee, B. S. Mordukhovich, and T. T. A. Nghia: Coderivative characterizations of maximal monotonicity for set-valued mappings, J. Convex Anal., 23, 461-480, 2016. ArXiv

16. B. S. Mordukhovich, T. T. A. Nghia, and R. T. Rockafellar: Full stability in finite-dimensional optimization, Math. Oper. Res., 40, 226-252, 2015. 

17. B. S. Mordukhovich and T. T. A. Nghia: Second-order characterizations of tilt stability with applications to nonlinear programming, Math. Program., 149, 83-104, 2015.

18. H. H. Bauschke, J. Y. Bello-Cruz, T. T. A. Nghia, H. M. Phan, and X. Wang: The rate of linear convergence of the Douglas-Rachford algorithm for subspaces is the cosine of the Friedrichs angle, J. Approx. Theory, 185, 63-79, 2014. arXiv

19. B. S. Mordukhovich and T. T. A. Nghia: Nonsmooth cone-constrained optimization with applications to semi-infinite programming, Math. Oper. Res., 39, 301-324, 2014.

20. D. Drusvyatskiy, B. S. Mordukhovich, and T. T. A. Nghia: Second-order growth, tilt stability, and metric regularity of the subdifferential, J. Convex Anal., 21, 1165-1192, 2014. arXiv

21. B. S. Mordukhovich and T. T. A. Nghia: Full Lipschitzian and Holderian stability in optimization with applications to mathematical programming and optimal control, SIAM J. Optim., 24, 1344-1381, 2014. 

22. T. T. A. Nghia: A note on implicit multifunction theorems, Optim. Letters, 8, 329-341, 2014. 

23. B. S. Mordukhovich and T. T. A. Nghia: Subdifferentials of non-convex supremum functions and their applications to semi-infinite and infinite programs with Lipschitzian data, SIAM J. Optim., 23, 406-431, 2013.

24. B. S. Mordukhovich and T. T. A. Nghia: Constraint qualifications and optimality conditions for nonconvex semi-infinite and infinite programs, Math. Program., 139, 271-300, 2013.

25. B. S. Mordukhovich and T. T. A. Nghia: Second-order variational analysis and characterizations of tilt-stable optimal solutions in infinite dimensional spaces, Nonlinear Anal., 86, 159-180, 2013. 

26. T. T. A. Nghia: A nondegenerate fuzzy optimality condition for constrained optimization problems without qualification conditions, Nonlinear Anal., 75, 6379-6390, 2012. 

27. B. S. Mordukhovich and T. T. A. Nghia: DC optimization approach to regularity of convex multifunctions with applications to infinite systems, J. Optim. Theory Appl., 155, 762-784, 2012. 

28. N. Dinh, B. S. Mordukhovich, and T. T. A. Nghia: Subdifferentials of value functions and optimality conditions for DC and bilevel infinite and semi-infinite programs, Math. Program., 123, 101-138, 2010. 

29. N. Dinh, T. T. A. Nghia and G. Vallet: A closedness condition and its applications to DC programs with convex constraints, Optimization, 59, 541-560, 2010.

30. N. Dinh, B. S. Mordukhovich, and T. T. A. Nghia: Qualification and optimality conditions for DC programs with infinite constraints, Acta Math. Vietnam, 34, 125-155, 2009. 

31. N. Dinh, T. T. A. Nghia and G. Vallet: Farkas-type results and duality for DC programs with convex constraints, J. Convex Anal., 15, 235-262, 2008. 

REFEREE SERVICE

SIAM Journal on Optimization, SIAM Journal on Control and Optimization, Mathematical Programming, Mathematics of Operations Research, Set-Valued and Variational Analysis, IEEE Control Systems, Journal of Computational and Applied Mathematics, Journal of Optimization Theory and Applications, Journal of Global Optimization, Positivity, Numerical Algorithms ...