Some dual conditions for global weak sharp minimality of nonconvex\n functions

2013/01/22 by Amos Uderzo, Uderzo, Amos
Computer Science · Mathematics · Engineering · #Optimization and Variational Analysis #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1301.5234

Abstract

Weak sharp minimality is a notion emerged in optimization, whose utility is\nlargeley recognized in the convergence analysis of algorithms for solving\nextremum problems as well as in the study of the perturbation behaviour of such\nproblems. In the present paper some dual constructions of nonsmooth analysis,\nmainly related to quasidifferential calculus and its recent developments, are\nemployed in formulating sufficient conditions for global weak sharp minimality.\nThey extend to nonconvex functions a condition, which is known to be valid in\nthe convex case. A feature distinguishing the results here proposed is that\nthey avoid to assume the Asplund property on the underlying space.\n

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