Subgradients  of  the optimal value  function   in a parametric discrete optimalcontrol problem

Nguyen Huy Chieu; Jen-Chih Yao

doi:10.3934/jimo.2010.6.401

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2010, Volume 6, Issue 2: 401-410. Doi: 10.3934/jimo.2010.6.401

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Subgradients of the optimal value function in a parametric discrete optimal control problem

Nguyen Huy Chieu^1, and
Jen-Chih Yao^2,

1.
Department of Mathematics, Vinh University, Vinh, Nghe An
2.
Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 804

Received: April 2009

Revised: January 2010

Published: April 2010

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Abstract

We study the first-order behavior of the optimal value function in a parametric discrete optimal control problem with linear constraints and a nonconvex cost function. By establishing a new result on the Fréchet subdifferential of optimal value functions of parametric mathematical programming problems, we obtain some formulae on the Fréchet subdifferential of optimal value functions in parametric discrete optimal control problems which complement results due to Kien et al. [3].

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Mathematics Subject Classification: Primary: 49K40, 49J52 ; Secondary: 49J53, 49M25.

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