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.
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