@article{10902/2200,
year = {2012},
url = {http://hdl.handle.net/10902/2200},
abstract = {An abstract optimization problem of minimizing a functional on a convex subset of a Banach space is considered. We discuss natural assumptions on the functional that permit establishing sufficient second-order optimality conditions with minimal gap with respect to the associated necessary ones. Though the two-norm discrepancy is taken into account, the obtained results exhibit the same formulation as the classical ones known from finite-dimensional optimization. We demonstrate that these assumptions are fulfilled, in particular, by important optimal control problems for partial differential equations. We prove that, in contrast to a widespread common belief, the standard second-order conditions formulated for these control problems imply strict local optimality of the controls not only in the sense of L ∞, but also of L2 .},
organization = {This author was supported by the Spanish Ministerio de Ciencia e Innovación under projects MTM2008-04206 and “Ingenio Mathematica (i-MATH)” CSD2006-00032 (Consolider Ingenio 2010)},
publisher = {Society for Industrial and Applied Mathematics},
publisher = {SIAM Journal on Optimization, 2012, 22(1), 261–279},
title = {Second order analysis for optimal control problems: improving results expected from abstract theory},
author = {Casas Rentería, Eduardo and Tröltzsch, Fredi},
}