State-Constrained Control-Affine Parabolic Problems I: First and Second Order Necessary Optimality Conditions
| Autor: | J. Frédéric Bonnans, Axel Kröner, M. Soledad Aronna |
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| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Numerical Analysis 021103 operations research Applied Mathematics 0211 other engineering and technologies Control variable Bilinear interpolation 010103 numerical & computational mathematics 02 engineering and technology State (functional analysis) Space (mathematics) Optimal control 01 natural sciences Applied mathematics Heat equation Geometry and Topology Affine transformation 0101 mathematics Analysis Variable (mathematics) Mathematics |
| Zdroj: | Set-Valued and Variational Analysis. 29:383-408 |
| ISSN: | 1877-0541 1877-0533 |
| DOI: | 10.1007/s11228-020-00560-2 |
| Popis: | In this paper we consider an optimal control problem governed by a semilinear heat equation with bilinear control-state terms and subject to control and state constraints. The state constraints are of integral type, the integral being with respect to the space variable. The control is multidimensional. The cost functional is of a tracking type and contains a linear term in the control variables. We derive second order necessary conditions relying on the concept of alternative costates and quasi-radial critical directions. The appendix provides an example illustrating the applicability of our results. |
| Databáze: | OpenAIRE |
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