CONTACT INFORMATION
Name: Nghia T. A. Tran
(Trần Thái An Nghĩa in Vietnamese, T. T. A. Nghia in publications)
Associate Professor
Department of Mathematics and Statistics,
Oakland University, Rochester, MI 48309, USA
Office: 444 MSC - Office phone: 248-370-4030
Email: nttran at oakland.edu
NT18.jpgRESEARCH INTERESTS
Nonsmooth Optimization, Variational Analysis, Mathematical Programming, Linear Inverse Problems
MathScinet Profile (authorized users)
Currently, I serve as an Associdate Editor for Set-Valued and Variational Analysis
Some hobbies: playing soccer, foosball, tennis, pickleball, ping pong and some guitar.
PUBLICATIONS
P. Hytla, T. T. A. Nghia, D. N. Phan, and A. Rice: A linearized alternating direction multiplier method for federated matrix completion problems, 2025, arXiv:2503.12733, submitted
Y. Cui, T. Hoheisel, T. T. A. Nghia, and D. Sun: Lipschitz stability of least-squares problems regularized by functions with C^2-cone reducible conjugates, 2024, arXiv:2409.13118, submitted.
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.
T. T. A. Nghia, H. N. Pham, and N. V. Vo: Stable recovery of regularized linear inverse problems, Inverse Problems, 41, 065018, 2025 arXiv:2412.11313.
J. Fadili, T. T. A. Nghia, and D. N. Phan: Solution uniqueness of convex optimization problems via the radial cone, J. Optim. Theory Appl., 206, 40 (2025), arXiv:2401.10346,
T. T. A. Nghia: Geometric characterizations of Lipschitz stability for convex optimization problems, SIAM J. Optim., 35(2), 2025, arXiv:2402.05215
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
J. Y. 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.
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.
J. Y. Bello-Cruz, G. Li, and T. T. A. Nghia: On the Q-linear convergence of forward-backward splitting method, J. Optim. Theory Appl., 188 , 378–401, 2021.
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.
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
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
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
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
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
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
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
B. S. Mordukhovich, T. T. A. Nghia, and R. T. Rockafellar: Full stability in finite-dimensional optimization, Math. Oper. Res., 40, 226-252, 2015.
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.
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
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.
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
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.
T. T. A. Nghia: A note on implicit multifunction theorems, Optim. Letters, 8, 329-341, 2014.
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.
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.
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.
T. T. A. Nghia: A nondegenerate fuzzy optimality condition for constrained optimization problems without qualification conditions, Nonlinear Anal., 75, 6379-6390, 2012.
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.
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.
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.
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.
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.