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Analysis of optimality conditions in time-optimal control problems governed by semilinear parabolic equations, highlighting KKT-type criteria.
A class of time-optimal control problems governed by semilinear parabolic equations with mixed pointwise constraints and final point constraints is considered. By introducing the locally optimal solution to time-optimal control problems, we derive first- and second-order necessary optimality conditions of KKT-type and second-order sufficient conditions for locally optimal solutions to the problem and establish regularity of Lagrange multipliers.
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Kien et al. (2025) studied this question.
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