Boundary bilinear control of semilinear parabolic PDEs: quadratic convergence of the SQP method

2025/05/30 by Casas, Eduardo, Mateos, Mariano
#35K58 #49K20 #49M05 #49M15 #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2505.24237

Abstract

We analyze a bilinear control problem governed by a semilinear parabolic equation. The control variable is the Robin coefficient on the boundary. First-order necessary and second-order sufficient optimality conditions are derived. A sequential quadratic programming algorithm is then proposed to compute local solutions. Starting the iterations from an initial point in an L²-neighborhood of the local solution we prove stability and quadratic convergence of the algorithm in L^p (p < ∞) and L^∞ assuming that the local solution satisfies a no-gap second-order sufficient optimality condition and a strict complementarity condition.

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