Second-order optimality conditions for weak and strong local solutions of parabolic optimal control problems

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URI: http://hdl.handle.net/10902/11155
ISSN: 2305-221X
ISSN: 2305-2228
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Autoría
Casas Rentería, EduardoAutoridad Unican; Tröltzsch, FrediAutoridad Unican
Fecha
2016-03
Derechos
© Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore. The final publication is available at Springer via https://doi.org/10.1007/s10013-015-0175-6
Publicado en
Vietnam Journal of Mathematics, 2016, 44(1), 181-202
Editorial
Springer Science + Business Media
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Palabras clave
Optimal control
Parabolic equations
Semilinear equation
Second order optimality conditions
Weak local minimum
Strong local minimum
Resumen/Abstract
Second-order sufficient optimality conditions are considered for a simplified class of semilinear parabolic equations with quadratic objective functional including distributed and terminal observation. Main emphasis is laid on problems where the objective functional does not include a Tikhonov regularization term. Here, standard second-order conditions cannot be expected to hold. For this case, new second-order conditions are established that are based on different types of critical cones. Depending on the choice of this cones, the second-order conditions are sufficient for local minima that are weak or strong in the sense of calculus of variations.
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