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

Le Quang Thuy () and Nguyen Thi Toan ()
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Le Quang Thuy: Hanoi University of Science and Technology
Nguyen Thi Toan: Hanoi University of Science and Technology

Journal of Optimization Theory and Applications, 2016, vol. 170, issue 1, No 3, 43-64

Abstract: 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.

Keywords: Parametric convex optimal control problem; Marginal function; Value function; Normal cone; Subdifferential; Singular subdifferential; 49J15; 49J53; 49K15; 90C90 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-016-0921-2

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