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 N. H. Chieu and L. V. Hien) Characterization of tilt stability via subgradient graphical derivative with applications to nonlinear programming (2017) arXiv:1705.09745
- (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,
(2016), to appear*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)- (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.** - (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) - (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- UML Applied Math Seminar, Lowell, MA, Nov 2016: 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 love playing Classical Guitar and cooking for family and friends. I play Soccer, Table Tennis, Chess occasionally; but my most favorite sport is Foosball, if you would like to have a game at Student Center for instance, contact me. "Work hard to find something that fascinates you" Richard P. Feynman |