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Research

I am interested in mathematical optimization, operations research, variational and convex analysis, and their applications. My research is partially supported by a KCS Seed Grant from a generous donor and by a gift from  

Publications

  1. Phan, D.-N., Bartz, S., Guha, N., Phan, H.M.: Stochastic variance-reduced majorization-minimization algorithms,
    SIAM Journal on Mathematics of Data Science 6, No.4, 926-952 (2024)
    DOI:10.1137/23M1571836    [arXiv:2305.06848]
  2. Bartz, S., Campoy, R., Phan, H.M.: An adaptive alternating direction method of multipliers,
    Journal of Optimization Theory and Applications 195, 1019-1055 (2022)
    DOI:10.1007/s10957-022-02098-9 (Open Access)   [arXiv:2103.07159]
  3. Dao, M.N., Phan, H.M.: An adaptive splitting algorithm for the sum of two generalized monotone operators and one cocoercive operator, Fixed Point Theory and Algorithms for Sciences and Engineering, Article 16 (2021)
    DOI:10.1186/s13663-021-00701-8 (Open Access)   [arXiv:2104.05460]
  4. Bartz, S., Dao, M.N., Phan, H.M.: Conical averagedness and convergence analysis of fixed point algorithms,
    Journal of Global Optimization 82, 351-373 (2022)
    DOI:10.1007/s10898-021-01057-4    [SharedIt]    [arXiv:1910.14185]
  5. Bartz, S., Bauschke, H.H., Phan, H.M., Wang, X.: Multi-marginal maximal monotonicity and convex analysis,
    Mathematical Programming Series A 185, 385-408 (2021)
    DOI:10.1007/s10107-019-01433-9   [SharedIt]   [arXiv:1901.03777]
  6. Bartz, S., Campoy, R., Phan, H.M.: Demiclosedness principles for generalized nonexpansive mappings,
    Journal of Optimization Theory and Applications 186(3), 759-778 (2020)
    DOI:10.1007/s10957-020-01734-6   [SharedIt]   [arXiv:2004.13778]
  7. Dao, M.N., Phan, H.M.: Computing the resolvent of the sum of operators with application to best approximation problems, Optimization Letters 14, 1193-1205 (2020)
    DOI:10.1007/s11590-019-01432-x   [SharedIt]    [arXiv:1809.03921]
  8. Dao, M.N., Phan, H.M.: Adaptive Douglas-Rachford splitting algorithm for the sum of two operators,
    SIAM Journal on Optimization 29(4), 2697-2724 (2019)
    DOI:10.1137/18M121160X   [official pdf]   [arXiv:1809.00761]
  9. Koch, V.R., Phan, H.M.: Optimization of triangular networks with spatial constraints,
    Optimization Methods and Software 36(4), 842-868 (2021)
    DOI:10.1080/10556788.2019.1604703   [arXiv:1811.04721]
  10. Bello-Cruz, J.Y., Díaz-Millán, R., Phan, H.M.: Conditional extragradient algorithms for variational inequalities,
    Pacific Journal of Optimization 15(3), 331-357 (2019)
    [article page]    [arXiv:1411.4338]
  11. Nam, N.M., Phan, H.M., Wang, B.: Bornological coderivative and subdifferential calculus in smooth Banach spaces,
    Set-Valued and Variational Analysis 27(4), 971-993 (2019)
    DOI:10.1007/s11228-018-0503-6   [SharedIt]  
  12. Dao, M.N., Phan, H.M.: Linear convergence of projection algorithms,
    Mathematics of Operations Research 44(2), 715-738 (2019)
    DOI:10.1287/moor.2018.0942   [arXiv:1609.00341]
  13. Dao, M.N., Phan, H.M.: Linear convergence of the generalized Douglas-Rachford algorithm for feasibility problems,
    Journal of Global Optimization 72(3), 443-474 (2018)
    DOI:10.1007/s10898-018-0654-x   [SharedIt]   [arXiv:1710.09814]
  14. Bauschke, H.H., Dao, M.N., Noll, D., Phan, H.M.: On Slater's condition and finite convergence of the Douglas-Rachford algorithm for solving convex feasibility problems in Euclidean spaces, Journal of Global Optimization 65(2), 329-349 (2016)
    DOI:10.1007/s10898-015-0373-5   [SharedIt]   [arXiv:1504.06969]
  15. Bauschke, H.H., Bello-Cruz, J.Y., Nghia, T.T.A., Phan, H.M., Wang, X.: Optimal rates of linear convergence of relaxed alternating projections and generalized Douglas-Rachford methods for two subspaces,
    Numerical Algorithms 73(1), 33-76 (2016)
    DOI:10.1007/s11075-015-0085-4   [arXiv:1407.0671]
  16. Bauschke, H.H., Koch, V.R., Phan, H.M.: Stadium norm and Douglas-Rachford splitting: a new approach to road design optimization, Operations Research 64(1), 201-218 (2016)
    DOI:10.1287/opre.2015.1427   [arXiv:1409.8244]
  17. Bauschke, H.H., Dao, M.N., Noll, D., Phan, H.M.: Proximal point algorithm, Douglas-Rachford algorithm and alternating projections: a case study, Journal of Convex Analysis 23(1), 237-261 (2016)    [article page]   [arXiv:1501.06603]
  18. Bauschke, H.H., Lucet, Y., Phan, H.M.: On the convexity of piecewise-defined functions,
    ESAIM: Control, Optimisation and Calculus of Variations 22(3), 728-742 (2016)    [article page]   [arXiv:1408.3771]
  19. Phan, H.M.: Linear convergence of the Douglas-Rachford method for two closed sets,
    Optimization 65(2), 369-385 (2016)    [article page]   [arXiv:1401.6509]
  20. Bauschke, H.H., Noll, D., Phan, H.M.: Linear and strong convergence of algorithms involving averaged nonexpansive operators, Journal of Mathematical Analysis and Applications 421(1), 1-20 (2015)    [article page]   [arXiv:1402.5460]
  21. Bauschke, H.H., Bello-Cruz, J.Y., Nghia, T.T.A., Phan, H.M., Wang, X.: The rate of linear convergence of the Douglas-Rachford algorithm for subspaces is the cosine of the Friedrichs angle,
    Journal of Approximation Theory 185, 63-79 (2014)    [article page]   [arXiv:1309.4709]
  22. Bauschke, H.H., Luke, D.R., Phan, H.M., Wang, X.: Restricted normal cones and sparsity optimization with affine constraints, Foundations of Computational Mathematics 14, 63-83 (2014)    [article page]   [arXiv:1205.0320]
  23. Bauschke, H.H., Phan, H.M., Wang, X.: The method of alternating relaxed projections for two nonconvex sets,
    Vietnam Journal of Mathematics 42, 421-450 (2014)    [article page]   [arXiv:1305.4296]
  24. Bauschke, H.H., Luke, D.R., Phan, H.M., Wang, X.: Restricted normal cones and the method of alternating projections: applications, Set-Valued and Variational Analysis 21, 475-501 (2013)    [article page]   [arXiv:1205.0318]
  25. Bauschke, H.H., Luke, D.R., Phan, H.M., Wang, X.: Restricted normal cones and the method of alternating projections: theory, Set-Valued and Variational Analysis 21, 431-473 (2013)    [article page]   [arXiv:1205.0318]
  26. Mordukhovich, B.S., Phan, H.M.: Tangential extremal principle for finite and infinite systems, II: applications to semi-infinite and multiobjective optimization, Mathematical Programming Series B 136, 31-63 (2012)    [article page]   [arXiv:1101.4176]
  27. Mordukhovich, B.S., Phan, H.M.: Tangential extremal principle for finite and infinite systems, I: basic theory,
    Mathematical Programming Series B 136, 3-30 (2012)    [article page]   [arXiv:1101.4178]
  28. Mordukhovich, B.S., Nam, N.M., Phan, H.M.: Variational analysis of marginal function and applications to bilevel programming problems, Journal of Optimization Theory and Application 152, 557-586 (2012)    [article page]
  29. Hoheisel, T., Kanzow, C., Mordukhovich, B.S., Phan, H.M.: Generalized Newton's method based on graphical derivatives, Nonlinear Analysis 75 (2012), 1324-1340    [article page]   [arXiv:1009.0410]
  30. Mordukhovich, B.S., Phan, H.M.: Rated extremal principle for finite and infinite systems with applications to optimization, Optimization 60(7), 893-924 (2011)    [article page]   [arXiv:1102.5304]
  31. Ph.D. Thesis: New Variational Principles with Applications in Optimization Theory and Algorithms
    Wayne State University Dissertations, Paper 327 (2011)    [article page]
    (Advisor: Prof. Boris S. Mordukhovich)

Patents


Preprints


Conferences and Presentations

List of conferences that I attended

Other Links



Last Update: August 2023

"If we knew what we were doing it wouldn't be research" (Albert Einstein)