Boundary Bilinear Control of Semilinear Parabolic PDEs: Quadratic Convergence of the SQP Method

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2026年6月16日

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Eduardo Casas,
Mariano Mateos

摘要

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 admissible initial control in an $L^2$ $L^{2}$ -neighborhood of the local solution we prove stability and quadratic convergence of the algorithm in $L^p$ $L^{p}$ ( $p < \infty $ $p < \infty$ ) and $L^\infty $ $L^{\infty}$ assuming that the local solution satisfies a no-gap second-order sufficient optimality condition and a strict complementarity condition.