CONTACT INFORMATION

Name: 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


EDUCATION

- 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.


RESEARCH INTERESTS

       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
  • arXiv:1708.06631
    (with N. H. Chieu and L. V. Hien) Characterization of tilt stability via subgradient graphical derivative with applications to nonlinear programming (2017), submitted 
    arXiv:1705.09745
  • (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, Math. Program. (2017), to appear (pdf)
  • (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. MordukhovichLocal monotonicity and full stability for parametric variational systems, SIAM J. Optim.  23, 1032-1059 (2016), (pdf)
  • (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. MordukhovichSecond-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 (2014) (pdf)
  • (with B. Mordukhovich) Full Lipschitzian and Holderian stability in optimization with applications to mathematical programming and optimal control, SIAM J. Optim.24, 1344-1381 (2014) (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 angleJ. Approx. Theory185, 63-79 (2014) (pdf)
  • A note on implicit multifunction theorems, Optim. Letters8, 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, SIAM J. Optim.23, 406-431 (2013) (pdf)
  • (with B. S. Mordukhovich) Constraint qualifications and optimality conditions for nonconvex semi-infinite and infinite programs, Math. Program., 139, 271-300 (2013) (pdf)
  • (with B. S. Mordukhovich) Second-order variational analysis and characterizations of tilt-stable optimal solutions in infinite dimensional spaces, Nonlinear Anal.86, 159-180 (2013) (pdf)
  • A nondegenerate fuzzy optimality condition for constrained optimization problems without qualification conditions, Nonlinear Anal.75,  6379-6390 (2012) (pdf)
  • (with B. S. Mordukhovich) DC optimization approach to regularity of convex multifunctions with applications to infinite systems, J. Optim. Theory Appl.155, 762-784 (2012) (pdf)
  • (with N. Dinh and B. S. Mordukhovich) Subdifferentials of value functions and optimality conditions for DC and bilevel infinite and semi-infinite programs, Math. Program.123, 101-138 (2010) (pdf)
  • (with N. Dinh and G. Vallet) A closedness condition and its applications to DC programs with convex constraints,    Optimization59, 541-560 (2010) (pdf)
  • (with N. Dinh and B. S. Mordukhovich) Qualification and optimality conditions for DC programs with infinite constraints,  Acta Math. Vietnam34,  125-155 (2009) (pdf)
  • (with N. Dinh and G. Vallet) Farkas-type results and duality for DC programs with convex constraints, J. Convex Anal.15, 235-262 (2008) (pdf)

 

REFEREE SERVICE


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, ... 


REVIEWER


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