vladimirsky@cornell.edu
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
No courses in 2018-19. On sabbatical leave at Princeton University.
Near Future:
Math 3610,
(The Art & Science of) Mathematical Modeling , Fall 2019.
Math 6230,
Differential Games, Optimal Control, Front Propogation, and Dynamic Programming , Fall 2019.
Previously taught.
Research Interests
My work so far has been in Numerical Analysis ,
Non-linear PDEs , and Dynamical Systems .
A brief description of several recent 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 & multi-modular optimization
* 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 ;
preliminary journal link. )
(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.
published on-line in
Journal of Scientific Computing (2019).
(preprint of accepted version)
Preprints
A. Vladimirsky and C. Zheng.
A fast implicit method for time-dependent Hamilton-Jacobi PDEs.
submitted to Communications in Applied Mathematics and Computational Science .
Z. Clawson, X. Ding, B. Englot, T.A. Frewen, W.M. Sisson, and A. Vladimirsky.
A bi-criteria path planning algorithm for robotics applications.
submitted to The International Journal of Robotics Research .
Z. Shen and A. Vladimirsky.
Piecewise-Deterministic Optimal Path Planning.
submitted to Journal of Optimization Theory and Applications .
M. Gluzman, J.G. Scott, and A. Vladimirsky.
Optimizing adaptive cancer therapy:
dynamic programming and evolutionary game theory.
submitted to British Journal of Cancer .
M.A. Gilles and A. Vladimirsky.
Surveillance-Evasion games under uncertainty.
submitted to Dynamic Games and Applications .
E. Cartee, L. Lai, Q. Song, and A. Vladimirsky.
Time-Dependent Surveillance-Evasion Games.
submitted to IEEE Control Systems Letters / CDC-2019 .
(Note:
■ bullets are used to mark refereed conference proceedings papers
and reviewed/published "extended abstracts".)
An outdated programming resume (from my days as a software consultant).