Regularity of multipliers and second-order optimality conditions for semilinear parabolic optimal control problems with mixed pointwise constraints

2023/06/17 by H. V. Khanh, Khanh, Huynh, B. T. Kien +1
Computer Science · Mathematics · #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Nonlinear Partial Differential Equations #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2306.10295

openalex publication_date 2023/06/17 · openalex created_date 2023/06/22 · openalex updated_date 2026/07/28

Abstract

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 L^p-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.

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