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Subgradients of the Value Function in a Parametric Convex Optimal Control Problem

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Abstract

Motivated by our recent works on the optimal value function in parametric optimal control problems under linear state equations, in this paper we study of the first-order behavior of the value function of a parametric convex optimal control problem with a convex cost function and linear state equations. By establishing an abstract result on the subdifferential of the value function to a parametric convex mathematical programming problem, we derive a formula for computing the subdifferential and the singular subdifferential of the value function to a parametric convex optimal control problem. By virtue of the convexity, several assumptions used in the above papers, like the existence of a local upper Lipschitzian selection of the solution map, as well as the V-inner semicontinuity of the solution map, are no longer needed.

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Acknowledgments

In this research, we were partially supported by the NAFOSTED 101.01-2015.04 of National Foundation for Science and Technology Development (Vietnam).

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Authors and Affiliations

  1. Hanoi University of Science and Technology, 1 Dai Co Viet, Hanoi, Vietnam

    Le Quang Thuy & Nguyen Thi Toan

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  1. Le Quang Thuy
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  2. Nguyen Thi Toan
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Correspondence to Nguyen Thi Toan.

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Communicated by Boris Vexler.

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Thuy, L.Q., Toan, N.T. Subgradients of the Value Function in a Parametric Convex Optimal Control Problem. J Optim Theory Appl 170, 43–64 (2016). https://doi.org/10.1007/s10957-016-0921-2

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  • DOI: https://doi.org/10.1007/s10957-016-0921-2

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