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.
Founder and co-organizer of the Cornell Mathematical Contest in Modeling.

Teaching

Present (Continuous) :

Math 3610, (The Art & Science of) Mathematical Modeling, Fall 2024.

Math 6230, Differential Games, Optimal Control, Front Propogation, and Dynamic Programming, Fall 2024.

Future (Indefinite) :

Math 4280, Introduction to Partial Differential Equations, Spring 2025.

Past (Perfect) :

Math 3620 / BIOEE 3620, Dynamic Models in Biology, Spring 2024.

Previously taught.

Research Interests

My work so far has been in Numerical Analysis, Non-linear PDEs, and Dynamical Systems.
A brief description of several older 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 * Uncertainty quantification * Reinforcement learning * Mathematical biology * 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.
  Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, PMLR 206:8448-8462 (2023).

• E.Cartee, A. Farah, A. Nellis, J. van Hook, and A. Vladimirsky.
  Quantifying and managing uncertainty in piecewise-deterministic Markov processes.
  SIAM/ASA Journal on Uncertainty Quantification 11/3: 814-847 (2023).

• M. Wang, N. Patnaik, A. Somalwar, J. Wu, and A. Vladimirsky.
  Risk-aware stochastic control of a sailboat.
  accepted by, presented at (& soon to be published in the proceedings of) ACC-2024.

• M. Wang, J.G. Scott, and A. Vladimirsky.
  Threshold-awareness in adaptive cancer therapy.
  PLOS Computational Biology 20/6: e1012165 (2024).
  (an earlier preprint, more examples, movies, source code)

• D. Qi, A. Dhillon, and A. Vladimirsky.
  Optimality and robustness in path-planning under initial uncertainty.
  accepted by Dynamic Games and Applications (2024).

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.

• M. Gaspard and A. Vladimirsky.
  Monotone Causality in Opportunistically Stochastic Shortest Path Problems.

• M. Gee and A. Vladimirsky.
  Occasionally Observed Piecewise-Deterministic Markov Processes.

• M. Wang, A. Vladimirsky, and A. Giometto.
  Overcoming toxicity: why boom-and-bust cycles are good for non-antagonistic microbes.

• M. Gee, N. Gonzalez-Granda, S. Joshi, N. Rudrapatna, A. Somalwar, S. Ellner, and A. Vladimirsky.
  Navigating the Landscape of Fear.

An outdated programming resume (from my days as a software consultant).