Some Applications of Linear Programming Formulations in Stochastic Control

Dan Goreac () and Oana-Silvia Serea ()
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Dan Goreac: Université Paris-Est
Oana-Silvia Serea: Université de Perpignan Via Domitia

Journal of Optimization Theory and Applications, 2012, vol. 155, issue 2, No 12, 572-593

Abstract: Abstract We present two applications of the linearization techniques in stochastic optimal control. In the first part, we show how the assumption of stability under concatenation for control processes can be dropped in the study of asymptotic stability domains. Generalizing Zubov’s method, the stability domain is then characterized as some level set of a semicontinuous generalized viscosity solution of the associated Hamilton–Jacobi–Bellman equation. In the second part, we extend our study to unbounded coefficients and apply the method to obtain a linear formulation for control problems whenever the state equation is a stochastic variational inequality.

Keywords: Stochastic control; Linear programming; HJB equations; Zubov’s method; Stochastic variational inequality (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10957-012-0080-z

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