Oana Silvia Serea
Field of work
In the following, I would like to describe my main research activities, covering several subjects of different nature, though having one theme in common: control and optimization. More precisely, my work concerns the investigation of non-regular optimal control problems and differential games and the associated Hamilton-Jacobi-Bellman partial differential equations as well as the regularity of value functions for non-regular optimization problems using a wide range of mathematical techniques. These highly non-linear settings are challenging, e.g., because the value function is not even continuous in general. Moreover, several applications exist, e.g., in mechanics (for reflected control problems), physics and chemistry (for supremum cost problems), biology (for piecewise deterministic processes), and economics (technology adoption problem, by-catch fisheries).
In addition, I would like to mention some perspectives and research projects dealing, for instance, with: differential variational inequalities, piecewise deterministic Markov processes, model predictive control, and numerical methods for stochastic differential algebraic equations.
Publications
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Reflected dynamics: Viscosity analysis for L∞ cost, relaxation and abstract dynamic programming
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Existence of Solutions Belonging to a Tube for Non-Convex Sweeping Processes
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Ky-Fan and Sion theorems for the lexicographic order and applications to vectorial games and min-max control problems
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Numerical optimal control for HIV prevention with dynamic budget allocation
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An Abel-type result for controlled piecewise deterministic Markov processes
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A note on the adaptive estimation of the differential entropy by wavelet methods
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Optimality Issues for a Class of Controlled Singularly Perturbed Stochastic Systems
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Min-max control problems via occupational measures
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Uniform asymptotics in the average continuous control of Piecewise Deterministic Markov Processes: vanishing approach
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Computation of viability kernels: a case study of by-catch fisheries
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Characterization of the optimal trajectories for the averaged dynamics associated to singularly perturbed control systems
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Sensitivity analysis for relaxed optimal control problems with final-state constraints
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An LP approach to dynamic programming principles for stochastic control problems with state constraints
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A note on linearization methods and dynamic programming principles for stochastic discontinuous control problems
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Linearization Techniques for Linf-Control Problems and Dynamic Programming Principles in Classical and Linf-Control Problems
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Linearization techniques for controlled piecewise deterministic Markov processes; application to Zubov's method
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Some applications of linear programming formulations in stochastic control
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Optimality conditions for reflecting boundary control problems
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Mayer and Optimal Stopping Stochastic Control Problems With Discontinuous Cost
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Differential games and Zubov’s method
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When can it be not optimal to adopt a new technology? A viability theory solution to a two‐stage optimal control problem of new technology adoption
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Discontinuous control problems for non-convex dynamics and near viability for singularly perturbed control systems
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The problem of optimal control with reflection studied through a linear optimization problem stated on occupational measures
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Primal-lower-nice property of value functions in optimization and control problems
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Reflected differential games
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24. Viscosity solutions for partial differential equations with Neumann type boundary conditions and some aspects of Aubry Mather theory
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Hamilton–Jacobi equations related with differential games with supremum cost
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Convergence of discontinuous value functions of singularly perturbed control systems with terminal or infimum cost
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Semiconcave solutions of partial differential inclusions
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On reflecting boundary problem for optimal control
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A viability approach for optimal control with infimum cost
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Discontinuous differential games and control systems with supremum cost