Regularity of multipliers and second-order optimality conditions of KKT-type for semilinear parabolic control problems

2023/09/04 by H. V. Khanh, Khanh, Huynh, B. T. Kien +1
Computer Science · Mathematics · #Contact Mechanics and Variational Inequalities #Optimization and Variational Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2309.01368

Abstract

A class of optimal control problems governed by semilinear parabolic equations with mixed constraints and a box constraint for control variable is considered. We show that if the separation condition is satisfied, then both optimality conditions of KKT-type and regularity of multipliers are fulfilled. 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.

Related

• Regularity of multipliers and second-order optimality conditions for semilinear parabolic optimal control problems with mixed pointwise constraints
• Second-order Optimality Conditions for Time-Optimal Control Problems Governed by Semilinear Parabolic Equations
• Localising optimality conditions for the linear optimal control of semilinear equations via concentration results for oscillating solutions of linear parabolic equations
• Locally Lipschitz stability of solutions to a parametric parabolic optimal control problem with mixed pointwise constraints
• Solution stability of parabolic optimal control problems with fixed state-distribution of the controls