Research – Variational Analysis and Optimization Lab

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;

Research Interest/Area of Expertise

Optimization, Optimal Control, Numerical Analysis, Nonlinear and Variational Analysis

PDEs, Statistics, Data Science, Deep Reinforcement Learning, and Applications

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Conferences and Seminars Organized:

Seminar on Variational Analysis and Optimization at UofM: Please click here to see more details.

Variational Analysis and Optimization Seminar Fall 2022 Winter 22, Thursdays 9 AM-10 AM (Virtual and Room # EH 2238) and Variational Analysis and Optimization Seminar, Fridays 9 AM-10 AM (Virtual and Room # EH 2238), University of Michigan, Ann Arbor.
Organizer of a mini-symposium at the 10th International Congress on Industrial and Applied Mathematics, Waseda University, Tokyo, Japan, August 20-25, 2023.
Organizer of a mini-symposium at the SIAM Conference on Control and Its Applications (CT23), Philadelphia, Pennsylvania, U.S, July 24 – 26, 2023.
Organizer of the conference New trends in applied optimization control with applications & Midwest Optimization Meeting, University of Michigan, Ann Arbor, MI, October 13-14, 2023.
Organizer of the mini-symposium Variational Analysis and Optimization, 2022 SIAM Great Lakes Section Annual Meeting, Wayne State University, MI, United States, September 24, 2022.
Chair of the section CT6 at the 2018 SIAM Great Lakes Section Annual Meeting (SIAM 2018), Wayne State University, MI, United States, April 21, 2018.
Chair of the session Experimental Mathematics and Numerical Analysis I at the Joint Mathematics Meetings in Denver, Colorado, January 18, 2020.

Research Group (UofM)

PhD Students: Yuzhou Mao, Chinmaya Kausik, University of Michigan

REU Student: Zhongqi Ma with the project Incorporating Domain Knowledge in Neural Network

Log(M) Students: Fall 2021: Tianyi Cheng, Matthew Nomura, Chang Wang; Fall 2022: Cruise Song, Elham Islam, Pranjal Sharma, Yurong Chen: University of Michigan

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.

Research Opportunity available for Students

Feel free to send me an email if you are interested.

If you are interested in working with me at the University of Michigan, please apply for the REU (Spring/Summer) or Log(M) (Fall, Winter) at the University of Michigan.

REU applications are welcome from students from all schools. You are paid a stipend of approximately $4,800 for 8 weeks during the summer to work with us in Ann Arbor. NSF-funded participants must be U.S. citizens or permanent residents. We may have a limited amount of funding for non-resident non-citizens.

Please click here for more information about the REU program in general as well as other sites.

If you are interested in seeing some of the available research projects, you may do so by clicking here.

Currently, I have one graduate student, three undergrad students from UofM for Log(M), one REU student from Cornell University, one REU from Rice University, and one from the University of Illinois at Urbana Champaign. Please let me know if you are interested in joining our team!