CONTACT INFORMATIONName: Nghia T.A. Tran (Trần Thái An Nghĩa in Vietnamese, T.T.A. Nghia in publications) Assistant Professor, Department of Mathematics and Statistics, Oakland University, Rochester, MI 48309, USA Office: 347 MSC - Office phone: 248-370-4030 Email: nttran at oakland.edu
- Ph.D. in Applied Mathematics, Department of Mathematics, Wayne State University, USA, August 2013. - M.S. in Mathematical Statistics, Department of Mathematics, Wayne State University, USA, August 2011. - B.S. in Mathematics (honors), Department of Mathematics and Computer Science, Hochiminh City University of Pedagogy, Vietnam, August 2006.
Optimization, Mathematical Programming, Variational Analysis PUBLICATIONS - (with J. Y. Bello Cruz and G. Li) On the Q-linear convergence of forward-backward splitting method and uniqueness of optimal solution to Lasso (2017), submitted (
__pdf__) - (with B.S. Mordukhovich and D. T. Pham) Full stability of general parametric variational systems (2017), submitted
(with N. H. Chieu and L. V. Hien) Characterization of tilt stability via subgradient graphical derivative with applications to nonlinear programming (2017), submitted arXiv:1705.09745arXiv:1708.06631 - (with G. Li, B. S. Mordukhovich, and T-S Pham) Error bounds for parametric polynomial systems with applications to higher-order stability analysis and convergence rate,
(2017), to appear (pdf)*Math. Program.* - (with J. Y. Bello Cruz) On the convergence of the proximal forward-backward splitting method with linesearches,
,*Optim. Method Softw.*__31__, 1209-1239 (2016), (__pdf__) - (with B. S. Mordukhovich) Local monotonicity and full stability for parametric variational systems, SIAM J. Optim.
__23__, 1032-1059 - (with H. Bauschke, J. Y. Bello Cruz, 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__) - (with N.H. Chieu, G.M. Lee, and B. Mordukhovich) Coderivative characterizations of maximal monotonicity for set-valued mappings,
,*J. Convex Anal.*__23__, 461-480 (2016) (__pdf__) - (with B. Mordukhovich and R. T. Rockafellar) Full stability in finite-dimensional optimization,
**Math. Oper. Res.,**__40__, 226-252 (2015) (__pdf__) - (with B. Mordukhovich) Second-order characterizations of tilt stability with applications to nonlinear programming
**Math. Program. A,**__149__, 83-104 (2015) (__pdf__) **(with B. S. Mordukhovich) Nonsmooth cone-constrained optimization with applications to semi-infinite programming,****Math Oper. Res.,**__39__, 301-324 (2014) (pdf)- (with D. Drusvyatskiy and B. Mordukhovich) Second-order growth, tilt stability, and metric regularity of the subdifferential,
,**J. Convex Anal.**__21__, 1165-1192__pdf__) **(with B. Mordukhovich) Full Lipschitzian and Holderian stability in optimization with applications to mathematical programming and optimal control,**, 24, 1344-1381 (2014) (**SIAM J. Optim.**__pdf__)**(with H. Bauschke, J. Y. Bello Cruz, H. M. Phan, 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__**,**__pdf__)**A note on implicit multifunction theorems,**,**Optim. Letters**__8__, 329-341 (2014) (__pdf)__- (with B. S. Mordukhovich) Subdifferentials of non-convex supremum functions and their applications to semi-infinite and infinite programs with Lipschitzian data,
, 23, 406-431 (2013) (**SIAM J. Optim.**__pdf__) - (with B. S. Mordukhovich) Constraint qualifications and optimality conditions for nonconvex semi-infinite and infinite programs,
139, 271-300 (2013) (**Math. Program.**,__pdf__) - (with B. S. Mordukhovich) Second-order variational analysis and characterizations of tilt-stable optimal solutions in infinite dimensional spaces,
, 86, 159-180 (2013) (**Nonlinear Anal.**__pdf__) - A nondegenerate fuzzy optimality condition for constrained optimization problems without qualification conditions,
, 75, 6379-6390 (2012) (**Nonlinear Anal.**__pdf__) - (with B. S. Mordukhovich) DC optimization approach to regularity of convex multifunctions with applications to infinite systems,
, 155, 762-784 (2012) (**J. Optim. Theory Appl.**__pdf__) - (with N. Dinh and B. S. Mordukhovich) Subdifferentials of value functions and optimality conditions for DC and bilevel infinite and semi-infinite programs,
, 123, 101-138 (2010) (**Math. Program.**__pdf__) - (with N. Dinh and G. Vallet) A closedness condition and its applications to DC programs with convex constraints,
,**Optimization**__59__, 541-560 (2010) (__pdf__) - (with N. Dinh and B. S. Mordukhovich) Qualification and optimality conditions for DC programs with infinite constraints,
, 34, 125-155 (2009) (**Acta Math. Vietnam**__pdf__) - (with N. Dinh and G. Vallet) Farkas-type results and duality for DC programs with convex constraints,
*J. Convex Anal.*__pdf__)
SIAM Journal on Optimization, Mathematical Programming, Mathematics of Operations Research, Set-Valued and Variational Analysis, Journal of Computational and Applied Mathematics, Journal of Optimization Theory and Applications, Journal of Global Optimization, ...
AMS Mathematical Reviews COURSES TAUGHT AT OAKLAND UNIVERSITY- Functional Analysis, MTH 651
- Nonlinear Optimization - MOR 555
- Linear and Integer Optimization - MOR 454/554.
- Introduction to Operations Research - ISE 330/MOR 330/MOR331.
- Introduction to Differential Equations with Matrix Algebra - APM 255.
- Multivariable Calculus - MTH 254.
- Calculus I - MTH 154
TALKS- Organizer of Midwest Meeting Optimization, Oakland University, Rochester, MI, Oct 2017.
- SIAM Great Lake Section, Oakland University, Rochester, MI, April 2017: On the linear convergence of the forward-backward splitting method.
- UML Applied Math Seminar, Lowell, MA, Nov 2016: On the linear convergence of the forward-backward splitting method.
- 5th International Conference on Continuous Optimization, Tokyo, Japan, Aug 2016. Invited talk: On the linear convergence of the forward-backward splitting method.
- UNSW Applied Math Seminar, New South Wales, Sydney, Aug 2016: On the linear convergence of the forward-backward splitting method.
- AMS Central Fall Sectional Meeting, Loyola University Chicago, Chicago, IL, Oct 2015. Talk: On the convergence of the proximal forward-backward splitting methods with line searches.
- 22nd International Symposium on Optimization, Pittsburgh, PA, USA, July 2015. Talk: Full stability of parametric variational systems. (Chair session: Variational Analysis in Stability of Variational Systems)
- SIAM Conference on Optimization, San Diego, CA, USA, May 2014. Invited talk: Coderivative characterizations of maximal monotonicity with applications to variational systems.
- Joint Mathematics Meeting, Baltimore, MA, USA, January 2014. Talk: Coderivative characterizations of local monotonicity with applications to variational systems.
- Centre for Optimization, Convex Analysis & Nonsmooth Analysis, University of British Columbia, Kelowna, BC, Canada, November 2013. Invited talk: Metric regularity of the subdifferential.
- West Coast Optimization Meeting, University of Victoria, Victoria, BC, Canada, October 2013. Invited talk: Holderian and Lipschitzian stability of variational systems.
- Modeling and Optimization: Theory and Applications, Lehigh University, Bethlehem, PA, USA, August 2013. Talk: Full stability in nonlinear optimization with applications to semidefinite programming.
- 14th Midwest Optimization Meeting, Western Michigan University, Kalamazoo, MI, USA, October 2012. Talk: Second-order variational analysis and characterizations of tilt-stable optimal solutions in finite and infinite dimensional spaces.
- 13th Midwest Optimization Meeting & Workshop on Large Scale Optimization and Applications, Field Institute, Toronto, Canada, October 2011. Talk: Subdifferentials of supremum Lipschitzian functions and its applications to nonsmooth semi-infinite and infinite programs.
- Joint Mathematics Meeting, New Orleans, PA, USA, January 2011. Invited Talk: Optimality conditions in semi-infinite and infinite programming.
- 12th Midwest Optimization Meeting, Wayne State University, Detroit, MI, USA, October 2010. Invited talk: DC Approach to regularity modulus of convex multifunction and its applications to infinite systems.
- CIMPA-UNESCO-VIETNAM School on Variational Inequalities and Related Problems, Institute of Mathematics, Hanoi, Vietnam, June 2010. Talk: Constraint qualifications and optimality conditions in nonlinear infinite and semi-infinite programs.
- 11th Midwest Optimization Meeting, Western Michigan University, Kalamazoo, MI, USA, October 2009. Talk: Regularity modulus of linear semi-infinite and infinite systems.
- 20th International Symposium of Mathematical Programming, Chicago, IL, USA, August 2009. Invited talk: Subdifferentials of value functions and optimality conditions for DC and bilevel infinite and semi-infinite programs.
- International School and Workshop on Variational Analysis, Santiago, Chile, November 2008. Poster: Subdifferentials of value functions and optimality conditions for DC and bilevel infinite and semi-infinite programs.
HOBBIES In sparse time I play soccer, (table) tennis, chess (occasionally); but my most favorite sport is foosball. "Work hard to find something that fascinates you" Richard P. Feynman |