Alexander Vladimirsky

Member of graduate programs in Mathematics, Applied Mathematics, Theoretical & Applied Mechanics, Computational Science & Engineering.
Co-organizer of the Scientific Computing and Numerics (SCAN) Seminar.
Co-organizer of the Cornell Mathematical Contest in Modeling.

Teaching

Present (Continuous) :

Math 6230, Differential Games, Optimal Control, Front Propogation, and Dynamic Programming, Spring 2023.

Future (Indefinite) :

Math 3610, (The Art & Science of) Mathematical Modeling, Fall 2023.

Math 6150, Partial Differential Equations, Fall 2023.

Past (Perfect) :

Math 3610, (The Art & Science of) Mathematical Modeling, Fall 2022.

Math 4250 / CS 4210 / Math 5250, Numerical Analysis and Differential Equations, Fall 2022.

Math 2930, Differential Equations for Engineers, Spring 2022.

Previously taught.

Research Interests

My work so far has been in Numerical Analysis, Non-linear PDEs, and Dynamical Systems.
A brief description of several projects can be found here.

What follows is an unsorted list of my other mathematical interests:

* Control Theory & Differential Games * Front Propagation Problems * Anisotropy & Homogenization * Bifurcation Theory * Dimension Reduction * Pareto & multimodal optimization * Mathematical modeling * Elimination Theory * Computability & Complexity * Approximate & Probabilistic Algorithms * Computational Geometry * Error Analysis

Publications

• J.A. Sethian and A. Vladimirsky.
  Fast methods for the Eikonal and related Hamilton-Jacobi equations on unstructured meshes. Proc. Natl. Acad. Sci. USA 97/11: 5699-5703 (2000).

• J.A. Sethian and A. Vladimirsky.
  Ordered upwind methods for static Hamilton-Jacobi equations. Proc. Natl. Acad. Sci. USA 98/20: 11069-11074 (2001).

• J.A. Sethian and A. Vladimirsky.
  Ordered Upwind Methods for Hybrid Control. 5th International Workshop, HSCC 2002, Stanford, CA, USA, March 25-27, 2002, Proceedings (LNCS 2289: 393-406).

• J.A. Sethian and A. Vladimirsky.
  Ordered Upwind Methods for Static Hamilton-Jacobi Equations: Theory & Algorithms.
  SIAM J. on Numerical Analysis 41/1: 325-363 (2003).
  The first version had previously appeared as Center for Pure and Applied Mathematics Technical Report PAM-792 (University of California, Berkeley) in May 2001.

• J. Guckenheimer and A. Vladimirsky.
  A fast method for approximating invariant manifolds.
  SIAM J. on Applied Dynamical Systems 3/3: 232-260 (2004).

• B. Krauskopf , H.M. Osinga, E.J. Doedel, M.E. Henderson, J. Guckenheimer, A. Vladimirsky, M. Dellnitz, and O. Junge.
  A survey of methods for computing (un)stable manifolds of vector fields.
  Int. J. Bifurcation and Chaos 15(3): 763-791 (2005).

• A. Vladimirsky.
  Static PDEs for Time-Dependent Control Problems.
  Interfaces and Free Boundaries 8/3: 281-300 (2006).

• Z. Ren, S.B. Pope, A. Vladimirsky, and J.M. Guckenheimer.
  The invariant constrained equilibrium edge preimage curve method for the dimension reduction of chemical kinetics. J. Chem. Phys. 124, 114111 (2006).
  (Small print: Copyright (2006) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.)

• Z. Ren, S.B. Pope, A. Vladimirsky, and J.M. Guckenheimer.
  Application of the ICE-PIC method for the dimension reduction of chemical kinetics coupled with transport.
  Proceedings of the Combustion Institute 31, 473-481 (2007).

• A. Vladimirsky.
  Label-setting methods for Multimode Stochastic Shortest Path problems on graphs.
  Mathematics of Operations Research 33(4): 821-838 (2008).

• T. Sahai and A. Vladimirsky.
  Numerical methods for approximating invariant manifolds of delayed systems.
  SIAM J. on Applied Dynamical Systems 8/3: 1116-1135 (2009).

• A.M. Oberman, R. Takei, and A. Vladimirsky.
  Homogenization of metric Hamilton-Jacobi equations.
  Multiscale Modeling and Simulation 8/1: 269-295 (2009).

• A. Kumar and A. Vladimirsky.
  An efficient method for multiobjective optimal control and optimal control subject to integral constraints.
  Journal of Computational Mathematics 28/4: 517-551 (2010).

• S. Li, S. Fomel, and A. Vladimirsky.
  Improving wave-equation fidelity of Gaussian beams by solving the complex eikonal equation.
  Society of Exploration Geophysicists Annual Meeting, (San Antonio, TX) 3829-3834, (2011).

• A. Chacon and A. Vladimirsky.
  Fast two-scale methods for Eikonal equations.
  a shortened version has been published by SIAM J. on Scientific Computing 34/2: A547-A578 (2012).

• S. Ermon, C. Gomes, B. Selman, and A. Vladimirsky.
  Probabilistic Planning with Non-Linear Utility Functions and Worst-Case Guarantees.
  Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems, Vol.2, 965-972 (2012).

• S. Li, S. Fomel, and A. Vladimirsky.
  Prestack first-break traveltime tomography using the double-square-root eikonal equation.
  Society of Exploration Geophysicists Annual Meeting, Las Vegas, NV (2012).

• V. Bashkardin, T. Browaeys, S. Fomel, F. Gao, R. Kazinnik, S. Morton, S. Terentyev, A. Vladimirsky, and P. Williamson.
  Phase-space computation of multi-arrival traveltimes, Part I: Theory and concepts.
  Society of Exploration Geophysicists Annual Meeting, Las Vegas, NV (2012).

• V. Bashkardin, T. Browaeys, S. Fomel, F. Gao, R. Kazinnik, S. Morton, S. Terentyev, and A. Vladimirsky.
  Phase-space computation of multi-arrival traveltimes: Part II - Implementation and application to angle-domain imaging.
  Society of Exploration Geophysicists Annual Meeting, Las Vegas, NV (2012).

• S. Li, A. Vladimirsky, and S. Fomel
  First-break Traveltime Tomography with the Double-square-root Eikonal Equation.
  Geophysics, vol. 78, U89-U101 (2013).

• J. Andrews and A. Vladimirsky.
  Deterministic control of randomly-terminated processes.
  Interfaces and Free Boundaries 16/1: 1-40 (2014).

• Z. Clawson, A. Chacon, and A. Vladimirsky.
  Causal domain restriction for Eikonal equations.
  SIAM J. on Scientific Computing 36/5: A2478-A2505 (2014).

• A. Chacon and A. Vladimirsky.
  A parallel two-scale method for Eikonal equations.
  SIAM J. on Scientific Computing 37/1: A156-A180 (2015).

• R. Takei, W. Chen, Z. Clawson, S. Kirov, and A. Vladimirsky.
  Optimal control with budget constraints and resets.
  SIAM J. on Control and Optimization 53/2: 712–744 (2015).

• A.Z. Palmer and A. Vladimirsky.
  Optimal Stopping with a Probabilistic Constraint.
  Journal of Optimization Theory and Applications 175/3: 795-817 (2017). (preprint; journal version -- free, but not printable.)
  (The final publication is available at Springer via https://doi.org/10.1007/s10957-017-1183-3.)

• E. Cartee and A. Vladimirsky.
  Anisotropic Challenges in Pedestrian Flow Modeling.
  Communications in Mathematical Sciences 16/4: 1067–1093 (2018).

• D. Qi and A. Vladimirsky.
  Corner cases, singularities, and dynamic factoring.
  Journal of Scientific Computing 79/3: 1456–1476 (2019). (preprint; journal version -- free, but not printable.)
  (The final publication is available at Springer via https://doi.org/10.1007/s10915-019-00905-6.)

• E. Cartee, L. Lai, Q. Song, and A. Vladimirsky.
  Time-Dependent Surveillance-Evasion Games.
  2019 IEEE 58th Conference on Decision and Control (CDC), Nice, France, 2019, pp. 7128-7133, doi: 10.1109/CDC40024.2019.9029329.

• M.A. Gilles and A. Vladimirsky.
  Evasive path planning under surveillance uncertainty.
  Dynamic Games and Applications 10/2: 391-416 (2020). (preprint; journal version -- free, but not printable.)
  (The final publication is available at Springer via https://doi.org/10.1007/s13235-019-00327-x.)

• E. Cartee and A. Vladimirsky.
  Control-Theoretic Models of Environmental Crime.
  SIAM J. on Applied Mathematics 80/3: 1441-1466 (2020).

• M. Gluzman, J.G. Scott, and A. Vladimirsky.
  Optimizing adaptive cancer therapy: dynamic programming and evolutionary game theory.
  Proceedings of the Royal Society B: Biological Sciences 287: 20192454 (2020). (an earlier preprint version).

• M. Gee and A. Vladimirsky.
  Optimal Path Planning with Random Breakdowns.
  IEEE Control Systems Letters 6: 1658-1663 (2021). (an earlier preprint version).

• C. Miles and A. Vladimirsky.
  Stochastic Optimal Control of a Sailboat.
  IEEE Control Systems Letters 6: 2048-2053 (2022).
  (an earlier preprint, more examples, movies, source code)

• M. Gaspard and A. Vladimirsky.
  Optimal Driving Under Traffic Signal Uncertainty.
  IFAC Workshop on Control Applications of Optimization;
  IFAC-PapersOnLine 55/16: 25-31, 2022.
  (an earlier preprint, more examples, movies, source code)

• D. Qi, D. Bindel, and A. Vladimirsky.
  Surveillance Evasion Through Bayesian Reinforcement Learning.
  accepted by AISTATS-2023; to appear in Proceedings of Machine Learning Research.

• E.Cartee, A. Farah, A. Nellis, J. van Hook, and A. Vladimirsky.
  Quantifying and managing uncertainty in piecewise-deterministic Markov processes.
  accepted; to appear in SIAM/ASA Journal on Uncertainty Quantification.

Preprints

• A. Vladimirsky and C. Zheng.
  A fast implicit method for time-dependent Hamilton-Jacobi PDEs.

• Z. Clawson, X. Ding, B. Englot, T.A. Frewen, W.M. Sisson, and A. Vladimirsky.
  A bi-criteria path planning algorithm for robotics applications.

• Z. Shen and A. Vladimirsky.
  Piecewise-Deterministic Optimal Path Planning.

• D. Qi, A. Dhillon, and A. Vladimirsky.
  Optimality and robustness in path-planning under initial uncertainty.

• M. Wang, J.G. Scott, and A. Vladimirsky.
  Stochastic optimal control to guide adaptive cancer therapy.

An outdated programming resume (from my days as a software consultant).