PENN STATE HBG

MIDDLETOWN, PA 17057

## Biography

Dr. Shvartsman graduated with a Bachelor's and Master's degrees in mathematics from Ural State University, Russia, in 1998 and obtained his Ph.D at Wayne State University, Detroit, MI, in 2003. In 2003-06 he worked as a postdoctoral researcher at Imperial College London and University of Bath in England. In 2006-07 he worked as a visiting assistant professor at Miami University of Ohio. Dr. Shvartsman has been with Penn State Harrisburg since 2007.

## Research Interests

- Optimal Control Theory
- Nonlinear and Nonsmooth Analysis

## Publications

V. Gaitsgory, I. Shvartsman, Averaging of a Class of Singularly Perturbed Control Systems: a Non-Asymptotic Result, Mathematics of Control Systems and Signals, to appear.

I. Shvartsman, Compactification Method in Linear Programming Approach to Infinite-Horizon Optimal Control Problems with a Noncompact State Constraint,Discrete and Continuous Dynamical Systems, Series B, Vol. 29 (1), 2024, pp. 110-123.

I. Shvartsman, Optimality Conditions in Infinite-Horizon Optimal Control Problem with Vanishing Discounting, Proceedings of the 62nd Conference on Decision and Control, 2023.

V. Gaitsgory, I. Shvartsman, Linear Programming Estimates for Cesaro and Abel Limits of Optimal Values in Optimal Control Problems, Discrete and Continuous Dynamical Systems, Series B, Vol 27(3), 2022, pp. 1591-1610.

V. Gaitsgory, I. Shvartsman, LP-Related Representations of Cesaro and Abel Limits of Optimal Value Functions, Optimization, Vol 71(4), 2022, pp. 1151-1170.

I. Shvartsman, Lack of Equality between Abel and Cesaro Limits in Discrete Optimal Control and the Implied Duality Gap, Pure and Applied Functional Analysis, Vol 6(6), 2021, pp. 1495-1507.

V. Borkar, V. Gaitsgory, I. Shvartsman, LP Formulations of Discrete Time Long-Run Average Optimal Control Problems: The Non-Ergodic Case, SIAM Journal on Control and Optimization, Vol 57(3), 2019, pp. 1783-1817.

V. Gaitsgory, A. Parkinson, I. Shvartsman, Linear Programming Based Optimality Conditions and Approximate Solution of a Deterministic Infinite Horizon Discounted Optimal Control Problem in Discrete Time, Discrete and Continuous Dynamical Systems, Series B, Vol 24(4), 2019, pp. 1743-1767.

I. Shvartsman, A Weighted Averages-Based Algorithm for a Numerical Solution of an Infinite Horizon Optimal Control Problem with Discounting in Discrete Time, Pure and Applied Functional Analysis, Vol 4(1), 2019.

V. Gaitsgory, A. Parkinson and I. Shvartsman, Linear Programming Formulations of Deterministic Infinite Horizon Optimal Control Problems in Discrete Time, Discrete and Continuous Dynamical Systems, Series B, Vol. 22(10), 2017, pp. 3821-3838.

A. Arutyunov, I. Shvartsman, Z. Zhukovskaya, Second-Order Optimality Conditions for Singular Extremals in Optimal Control Problems with Equality Endpoint Constraints, Nonlinear Analysis: Theory, Methods and Applications, Vol. 157, 2017, pp. 20-43.

Z. Mingaleeva, I. Shvartsman, Second Order Optimality Conditions for Singular Controls, Numerical Functional Analysis and Optimization, Vol. 35, 2014, pp. 1245-1257.

A. Arutyunov, A. Izmailov, I. Shvartsman, Optimality Conditions for 2-Regular Problems with Nonsmooth Objective Functions, Nonlinear Analysis: Theory, Methods and Applications, Vol. 90, 2013, pp. 37-45.

B.S. Mordukhovich, I. Shvartsman, Approximate Maximum Principle for Discrete Approximations of Optimal Control Systems with Nonsmooth Objectives and Endpoint Constraints, ESAIM: Control, Optimisation, and Calculus of Variations, Vol. 19(3), 2013, pp. 811-827.

I. Shvartsman, Necessary Optimality Conditions in Discrete Nonsmooth Optimal Control, Journal of Optimization Theory and Applications, Vol. 153(3), 2012, pp. 578-586.

I. Shvartsman, V. Chinchilli, H. Liu, A Frailty Model in Crossover Studies with Time-to-Event Response Variable, Communications in Statistics: Simulation and Computation, Vol 41, 2012, pp.1960-1969.

I. Shvartsman, On Sensitivity of Minimizers in Convex Programming, Nonlinear Analysis: Theory, Methods and Applications, Vol. 75(3), 2012, pp. 1563-1571.

M.R. de Pinho, I. Shvartsman, Lipschitz Continuity of Optimal Control in a Problem with Mixed and Pure State Constraints, Discrete and Continuous Dynamical Systems, Series A, Vol. 29(2), 2011, pp.505-522.

I. Shvartsman, Application of Variational Analysis and Control Theory to Non-Parametric Maximum Likelihood Estimation of a Probability Density Function, in R. Burachik, J. Yao, Editors, Variational Analysis and Generalized Differentiation in Optimization and Control, Springer, New York, 2010, pp.187-203.

H. Logemann, E.P. Ryan, I. Shvartsman, A Class of Differential-Delay Systems with Hysteresis: Asymptotic Behaviour of Solutions, Nonlinear Analysis: Theory, Methods and Applications, Vol. 69(1), 2008, pp. 363-391

I. Shvartsman, New Approximation Method in the Proof of the Maximum Principle for Nonsmooth Optimal Control Problems with State Constraints, J. of Mathematical Analysis and Applications, Vol. 326, 2007, pp. 974-1000

H. Logemann, E.P. Ryan, I. Shvartsman, Integral control in the presence of hysteresis: an input-output approach, ESAIM: Control, Optimisation and Calculus of Variations, Vol. 13(3), 2007, pp. 458-483

I. Shvartsman, R.B. Vinter, Regularity Properties of Optimal Controls for State Constrained Problems with Time-Varying Control Constraints, Nonlinear Analysis, Vol. 65(2), 2006, pp. 448-474.

I. Shvartsman, Finite-Dimensional Approximations in Necessary Optimality Conditions in Nonsmooth Constrained Optimal Control, Nonlinear Analysis: Theory, Methods and Applications, Vol. 63(5-7), 2005, pp. 1665-1672.

B.S. Mordukhovich, I. Shvartsman, The Approximate Maximum Principle in Constrained Optimal Control, SIAM Journal on Control and Optimization, Vol. 43(3), 2004, pp.1037 – 1062.

B.S. Mordukhovich, I. Shvartsman, Optimization and Feedback Control of Constrained Parabolic Systems under Uncertain Perturbations, in de Queiroz, M., M. Malisoff, and P. Wolenski, Editors, Optimal Control, Stabilization, and Nonsmooth Analysis, Lecture Notes in Control and Information Sciences, Springer-Verlag, Heidelberg, 2004, Vol.301, pp.121-132.

B.S. Mordukhovich, I. Shvartsman, Discrete Maximum Principle for Nonsmooth Optimal Control Problems with Delays, Cybernetics and System Analysis, No.2, 2002, pp. 245-254.

## Education

B.Sc.; M.Sc.; Ph.D. (Wayne State)