@article{10902/18552,
year = {2020},
month = {2},
url = {http://hdl.handle.net/10902/18552},
abstract = {In this paper, we analyze optimal control problems governed by semilinear parabolic equations. Box constraints for the controls are imposed, and the cost functional involves the state and possibly a sparsity-promoting term, but not a Tikhonov regularization term. Unlike finite dimensional optimization or control problems involving Tikhonov regularization, second order sufficient optimality conditions for the control problems we deal with must be imposed in a cone larger than the one used to obtain necessary conditions. Different extensions of this cone have been proposed in the literature for different kinds of minima: strong or weak minimizers for optimal control problems. After a discussion on these extensions, we propose a new extended cone smaller than those considered until now. We prove that a second order condition based on this new cone is sufficient for a strong local minimum.},
organization = {The authors were partially supported by Spanish Ministerio de Economía y Competitividad under research project MTM2017-83185-P.},
publisher = {Society for Industrial and Applied Mathematics},
publisher = {SIAM Journal on Optimization, 2020, 30(1), 585-603 - (CORRIGENDUM), 2022, 32(1), 319-320},
title = {Critical cones for sufficient second order conditions in PDE constrained optimization},
author = {Casas Rentería, Eduardo and Mateos Alberdi, Mariano},
}