Second-order optimality conditions for weak and strong local solutions of parabolic optimal control problems
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2016-03Abstract
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.
Palabras clave
Optimal control
Parabolic equations
Semilinear equation
Second order optimality conditions
Weak local minimum
Strong local minimum
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
Publisher
Springer Science + Business Media
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