Work

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

Year: 2026

Type: article

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 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 < ∞ ) and $$L^\infty $$ L ∞ assuming that the local solution satisfies a no-gap second-order sufficient optimality condition and a strict complementarity condition.

Source: Applied Mathematics & Optimization

DOI: 10.1007/s00245-026-10454-8

Authors: Eduardo Casas, Mariano Mateos

Institutions: Universidad de Cantabria, Universidad de Oviedo

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,890

Funder: Agencia Estatal de Investigación