Regularity of Multipliers and Second-Order Optimality Conditions for Semilinear Parabolic Optimal Control Problems with Mixed Pointwise Constraints
H. V. Khanh, B. T. Kien · Numerical Functional Analysis and Optimization · 2024
A class of optimal control problems governed by semilinear parabolic equations with mixed pointwise constraints is considered. We give some criteria under which the first and second-order optimality conditions are of KKT-type. We then prove that the Lagrange multipliers belong to Lp-spaces. Moreover, we show that if the initial value is good enough and boundary ∂Ω has a property of positive geometric density, then multipliers and optimal solutions are Hölder continuous.