Research

Research Statement

Research Grants

  • Simon Foundations Grant (2022-2024).
  • NSF conference grant $25,000: https://emunix.emich.edu/~bwang/MOM2023/index.html. We are sincerely grateful to the NSF for their support and trust in our project. Thanks to Professor Boris Mordukhovich and Ebrahim Sarabi for the collaboration in this proposal.
  • Research of this author was partly supported by the USA National Science Foundation under grant DMS-1808978, DMS-1743826, DMS-1512846, the USA Air Force Office of Scientific Research grant #15RT0462, and the EDES grant number REDI170200.
  • PI of four pending NSF Proposals (MSPRF, Applied Mathematics, Probability, and NSF Conferences — 2022).
  • PI of a NSF Proposal with Agency Tracking Number 2205693 submitted on 11/12/2021 under Regents University of Michigan ($295,463). Review: V/G,G,G;

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Published, Accepted Journal Papers 

  • (with G. Colombo and B. S. Mordukhovich) Optimization of a perturbed sweeping process by discontinuous controls, SIAM J. Control Optim., 58 (2020), 2678-2709.
  • (with G. Colombo and B. S. Mordukhovich) Optimal Control of Sweeping Processes in Robotics and Traffic Flow Models, J. Optim. Theory Appl. 182 (2019), 439-472.
  • (with Tan Cao, G. Colombo, and B. S. Mordukhovich) Optimization and Discrete Approximation of Sweeping Processes with Controlled Moving Sets and Perturbations, J. Diff. Eqs. 274 (2021), 461-509.
  • (with B. S. Mordukhovich) Discrete Approximations and Optimal Control of Nonsmooth Perturbed Sweeping Processes, J. Convex Anal. 28 (2021), No. 2.
  • (with Tan Cao, G. Colombo, and B. S. Mordukhovich) Discrete Approximations of a controlled sweeping process over polyhedral sets with perturbations, to appear in J. Diff. Eqs. (2020), http://arxiv.org/abs/2012.11722.
  • (with T. H. Cao, G. Colombo, B. S. Mordukhovich, and T. Nguyen)  Applications of controlled sweeping processes to nonlinear crowd motion models with obstacles, to appear in IEEE Syst. Cont. Lett. (2021); arXiv:2104.03444.
  • (with T. H. Cao, N. T. Khalil, B. S. Mordukhovich, and F. L. Pereira) Crowd model paradigm modeled by bilevel optimal control, to appear in IEEE Syst. Cont. Lett. (2021); arxiv:2104.09673.
  • (with T. H. Cao, N. T. Khalil, B. S. Mordukhovich, T. Nguyen, and F. L. Pereira) Optimization of controlled free-time sweeping processes with applications to marine surface vehicle modeling, to appear in IEEE Syst. Cont. Lett. (2021); arXiv:2105.03490v1.
  • (with Harbir Antil, Rafael Arndt, Boris Mordukhovich and Carlos N. Rautenberg) Stability of the Solution Set of Quasi-variational Inequalities and Optimal Control, submitted, 2022, https://arxiv.org/abs/2209.00075.
  • Spot drilling time optimization for a cyclotron-based proton therapy system ( with Lewei Zhao, Sophie Wuyckens, Juntao You, Gang Liu, Xiliang Lu, Boris Mordukhovich, Xuanfeng Ding), submitted, 2023.
  • Model Predictive Control using Neural Network, Dao Nguyen, 2023.
  • (with Boris Mordukhovich and Trang Nguyen), Optimal control of sweeping processes in unmanned surface vehicles and nanoparticle modeling, submitted (2023); arXiv:2311.12916
  • (with G. Colombo, Boris Mordukhovich and T. Nguyen), Discrete approximations and optimality conditions for controlled free-time sweeping processes, submitted (2023); arXiv:2310.10782
  • (with T. H. Cao, B. S. Mordukhovich, T. Nguyen) Optimization and finite difference approximation of perturbed sweeping processes with variable time, submitted to J. Diff. Eqs. (2024).
  • (with B. S. Mordukhovich, T. Nguyen, N. Ortiz-Robinson and V. Ríos) Well-posedness and stability of discrete approximations for controlled sweeping processes with time delay, submitted to J. Optim. Theory Appl. (2024).https://arxiv.org/abs/2409.20404
  • (with G. Colombo et al.) Optimal control of perturbed sweeping process with applications to general robotic models, submitted to J. Optim. Theory Appl. (2024). https://arxiv.org/abs/2405.08986.
  • (with B. S. Mordukhovich and T. Nguyen) Optimal control of sweeping processes in unmanned surface vehicle and nanoparticle modeling, Optimization, 1-33, (2024). https://doi.org/10.1080/02331934.2024.2366832.
  • (with G. Colombo, B. S. Mordukhovich and T. Nguyen) Discrete approximations and optimality conditions for controlled free-time sweeping processes, Appl. Math. Optim. 89, 40 (2024). https://doi.org/10.1007/s00245-024-10108-7

Preprints & Current Projects

  • (with Boris S. Mordukhovich, Trang Nguyen (PhD student), and Norma O. Robinson) Numerical Methods and Practical Models of Optimal Control of Sweeping Processes, in preparation.
  • (with Fernando, Nathalie, Tan H. Cao, Boris S. Mordukhovich) On an optimal bilevel sweeping control problem, in preparation.
  • (with Boris S. Mordukhovich) Optimal Control of Nonsmooth Perturbed Sweeping Processes and Applications on Nanoparticles in Straight Tubes Model, in preparation.
  • (with Boris S. Mordukhovich and Qinghui Zhang) Optimal Control in PDEs.
  • (with Tan Cao and Tahar Haddad) Optimal Control for Impulsive Sweeping Processes, in preparation.
  • (with Tan Cao and Emilio Vilches) Optimal Control of ODEs System with Hysteresis via Discrete Approximations, in preparation.
  • Optimization for Sweeping Processes and Applications in Reinforcement Learning, in preparation.

Books & Lecture Notes

  1. Foundations of Machine Learning D. Nguyen Cognella Academic Publishing, textbook in preparation. PDF
  2. Applied Linear Regression D. Nguyen Textbook manuscript (lecture notes) supporting a proposed new course at SDSU, in preparation.

Refereed Journal Articles

Authors are listed alphabetically. Underlined names are student collaborators supervised or co-supervised by Dao Nguyen. Click a title to open the paper.

  1. Optimization of a perturbed implicit sweeping process by constrained discontinuous controls Y. Dang, B. S. Mordukhovich, D. Nguyen Submitted to Journal of Differential Equations, 2026.
  2. Well-posedness of a time-delayed sweeping process with a controlled polyhedral set D. Nguyen, Thang Nguyen Submitted to Applied Mathematics and Optimization, 2026.
  3. Learning-enhanced model predictive control for a differential-drive robot via iLQR warm starts and residual neural correction H. Arora, N. Le, D. Nguyen, J. Nie Submitted to IEEE Control Systems Letters, 2026.
  4. Generalization of learned UAV dynamics models under unseen flight conditions T. Ho, T. Le, D. Nguyen Submitted to IEEE Robotics and Automation Letters, 2026.
  5. ELOSPAT alternative: non-convex L1,1/2 norm optimization for proton arc therapy Huynh Khoi Minh Uyen, D. Nguyen In preparation.
  6. Optimal control of ODE systems with hysteresis via discrete approximations T. H. Cao, D. Nguyen, E. Vilches In preparation.
  7. Optimization for sweeping processes and applications in reinforcement learning D. Nguyen In preparation.
  8. Semicontinuity conditions in parametric set optimization problems with applications L. Q. Anh, L. V. Day, L. T. V. Khanh, T. T. T. Mai, D. Nguyen Submitted to Vietnam Journal of Mathematics, 2026.
  9. Stochastic gradient calibration of neural network-driven interacting particle systems E. Lester, D. Nguyen Submitted, 2026. PDF
  10. Optimal control of nonconvex sweeping processes with variable time via finite-difference approximations T. H. Cao, B. S. Mordukhovich, D. Nguyen, T. Nguyen, N. N. Thieu Nonlinear Analysis: Hybrid Systems 61 (2026), Article 101755. DOI arXiv
  11. Optimal control of perturbed sweeping processes with applications to general robotics models G. Colombo, B. S. Mordukhovich, D. Nguyen, T. Nguyen, N. Ortiz-Robinson Journal of Optimization Theory and Applications 208 (2026), Article 114. DOI arXiv
  12. Optimal control of a quasi-variational sweeping process H. Antil, R. Arndt, B. S. Mordukhovich, D. Nguyen, C. N. Rautenberg Mathematical Control and Related Fields 16 (2026), 132–156. DOI
  13. Well-posedness and stability of discrete approximations for controlled sweeping processes with time delay B. S. Mordukhovich, D. Nguyen, T. Nguyen, N. Ortiz-Robinson, V. Ríos Journal of Optimization Theory and Applications 206 (2025), Article 70. DOI arXiv
  14. Optimal control of sweeping processes in unmanned surface vehicle and nanoparticle modeling B. S. Mordukhovich, D. Nguyen, T. Nguyen Optimization 75 (2026), 2819–2851 (published online 2024). DOI arXiv
  15. Discrete approximations and optimality conditions for controlled free-time sweeping processes G. Colombo, B. S. Mordukhovich, D. Nguyen, T. Nguyen Applied Mathematics and Optimization 89 (2024), Article 40. DOI arXiv
  16. Spot drilling time optimization for a cyclotron-based proton therapy system L. Zhao, S. Wuyckens, J. You, G. Liu, X. Lu, B. S. Mordukhovich, X. Ding, D. Nguyen 61st PTCOG Conference, Madrid, Spain, 2023.
  17. Optimization of controlled free-time sweeping processes with applications to marine surface vehicle modeling T. H. Cao, N. T. Khalil, B. S. Mordukhovich, D. Nguyen, T. Nguyen, F. L. Pereira IEEE Control Systems Letters 6 (2022), 782–787. DOI arXiv
  18. Applications of controlled sweeping processes to nonlinear crowd motion models with obstacles T. H. Cao, B. S. Mordukhovich, D. Nguyen, T. Nguyen IEEE Control Systems Letters 6 (2022), 740–745. DOI arXiv
  19. Crowd motion paradigm modeled by a bilevel sweeping control problem T. H. Cao, N. T. Khalil, B. S. Mordukhovich, D. Nguyen, F. L. Pereira IEEE Control Systems Letters 6 (2022), 385–390. DOI arXiv
  20. Optimization of fully controlled sweeping processes T. H. Cao, G. Colombo, B. S. Mordukhovich, D. Nguyen Journal of Differential Equations 295 (2021), 138–186. DOI
  21. Optimization and discrete approximation of sweeping processes with controlled moving sets and perturbations T. H. Cao, G. Colombo, B. S. Mordukhovich, D. Nguyen Journal of Differential Equations 274 (2021), 461–509. DOI
  22. Discrete approximations and optimal control of nonsmooth perturbed sweeping processes B. S. Mordukhovich, D. Nguyen Journal of Convex Analysis 28 (2021), No. 2, 655–688. DOI
  23. Optimization of a perturbed sweeping process by constrained discontinuous controls G. Colombo, B. S. Mordukhovich, D. Nguyen SIAM Journal on Control and Optimization 58 (2020), 2678–2709. DOI
  24. Optimal control of sweeping processes in robotics and traffic flow models G. Colombo, B. S. Mordukhovich, D. Nguyen Journal of Optimization Theory and Applications 182 (2019), 439–472. DOI arXiv

Theses

Ph.D. dissertation of Dao Nguyen and M.S. theses supervised at San Diego State University.

  1. Stochastic gradient descent for traffic and pedestrian models via neural network and parameter identification Edward Lester — M.S. Thesis, advisor: D. Nguyen San Diego State University, defended August 2025. Thesis
  2. Optimization for controlled sweeping processes and applications Yen Dang — M.S. Thesis, advisor: D. Nguyen San Diego State University, 2026. Thesis
  3. Optimization of controlled sweeping processes with applications Nguyen-Truc-Dao Nguyen — Ph.D. Dissertation, advisor: B. S. Mordukhovich Wayne State University, 2021. Dissertation

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