On the No-Gap Second-Order Optimality Conditions for a Discrete Optimal Control Problem with Mixed Constraints

Le Quang Thuy (), Bui Thi Thanh () and Nguyen Thi Toan ()
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Le Quang Thuy: Hanoi University of Science and Technology
Bui Thi Thanh: Nghe An College of Economics
Nguyen Thi Toan: Hanoi University of Science and Technology

Journal of Optimization Theory and Applications, 2017, vol. 173, issue 2, No 3, 442 pages

Abstract: Abstract Motivated by our recent works on optimality conditions in discrete optimal control problems under a nonconvex cost function, in this paper, we study second-order necessary and sufficient optimality conditions for a discrete optimal control problem with a nonconvex cost function and state-control constraints. By establishing an abstract result on second-order optimality conditions for a mathematical programming problem, we derive second-order necessary and sufficient optimality conditions for a discrete optimal control problem. Using a common critical cone for both the second-order necessary and sufficient optimality conditions, we obtain “no-gap” between second-order optimality conditions.

Keywords: Second-order necessary optimality condition; Second-order sufficient optimality condition; No-gap second-order optimality condition; Discrete optimal control problem; Mixed constraint; 49J21; 93C55; 90C90 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-017-1094-3

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