Boundary Bilinear Control of Semilinear Parabolic PDEs: Quadratic Convergence of the SQP Method
Abstract
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.
Fields of Study & Subjects
Advanced Numerical Methods in Computational Mathematics
Stability and Controllability of Differential Equations
Numerical methods for differential equations
Publication details
- Journal / source
- Applied Mathematics & Optimization
- Publisher
- Springer Science and Business Media LLC
- Volume
- 94
- Issue
- 1
- Publication date
- 16 June 2026
- Language
- EN