Second-order KKT optimality conditions for multiobjective discrete optimal control problems

Nguyen Thi Toan (), Le Quang Thuy (), Nguyen Tuyen () and Yi-Bin Xiao ()
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Nguyen Thi Toan: Hanoi University of Science and Technology
Le Quang Thuy: Hanoi University of Science and Technology
Nguyen Tuyen: University of Electronic Science and Technology of China
Yi-Bin Xiao: University of Electronic Science and Technology of China

Journal of Global Optimization, 2021, vol. 79, issue 1, No 8, 203-231

Abstract: Abstract This paper deals with second-order necessary and sufficient optimality conditions of Karush–Kuhn–Tucker-type for local optimal solutions in the sense of Pareto to a class of multi-objective discrete optimal control problems with nonconvex cost functions and state-control constraints. By establishing an abstract result on second-order optimality conditions for a multi-objective mathematical programming problem, we derive second-order necessary and sufficient optimality conditions for a multi-objective 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; Multi-objective discrete optimal control problem; Mixed constraint; 49K40; 49J53; 90B50; 58E17; 34H05 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10898-020-00935-7

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