Boundary bilinear control of semilinear parabolic PDEs: quadratic convergence of the SQP method
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908978803376128 |
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| author | Casas, Eduardo Mateos, Mariano |
| author_facet | Casas, Eduardo Mateos, Mariano |
| contents | 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 $L^2$-neighborhood of the local solution we prove stability and quadratic convergence of the algorithm in $L^p$ ($p < \infty$) and $L^\infty$ assuming that the local solution satisfies a no-gap second-order sufficient optimality condition and a strict complementarity condition. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_24237 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Boundary bilinear control of semilinear parabolic PDEs: quadratic convergence of the SQP method Casas, Eduardo Mateos, Mariano Optimization and Control Analysis of PDEs 35K58, 49K20, 49M15, 49M05 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 $L^2$-neighborhood of the local solution we prove stability and quadratic convergence of the algorithm in $L^p$ ($p < \infty$) and $L^\infty$ assuming that the local solution satisfies a no-gap second-order sufficient optimality condition and a strict complementarity condition. |
| title | Boundary bilinear control of semilinear parabolic PDEs: quadratic convergence of the SQP method |
| topic | Optimization and Control Analysis of PDEs 35K58, 49K20, 49M15, 49M05 |
| url | https://arxiv.org/abs/2505.24237 |