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Stationarity and regularity of infinite collections of sets. Applications to infinitely constrained optimization

Alexander Y. Kruger (a.kruger***at***ballarat.edu.au)
Marco A. López (marco.antonio***at***ua.es)

Abstract: This article continues the investigation of stationarity and regularity properties of infinite collections of sets in a Banach space started in Kruger & L�pez (2012) and is mainly focused on the application of the criteria from Kruger & L�pez (2012) to infinitely constrained optimization problems. We consider several settings of optimization problems which involve (explicitly or implicitly) infinite collections of sets and deduce for them necessary conditions characterizing stationarity in terms of dual space elements - normals and/or subdifferentials.

Keywords: subdifferential, normal cone, optimality, extremality, stationarity, regularity, slope, Asplund space, infinitely constrained optimization

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 2: Infinite Dimensional Optimization (Semi-infinite Programming )

Citation: Published in Journal of Optimization Theory and Applications (2012) 155(2):390–416. The original publication is available at http://link.springer.com/article/10.1007%2Fs10957-012-0086-6

Download: [PDF]

Entry Submitted: 12/19/2011
Entry Accepted: 12/19/2011
Entry Last Modified: 11/12/2012

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