Generalized weak sharp minima in cone‐constrained convex optimization with applications

Generalized weak sharp minima in cone‐constrained convex optimization with applications

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Article ID: iaor20128211
Volume: 53
Issue: 3
Start Page Number: 807
End Page Number: 821
Publication Date: Dec 2012
Journal: Computational Optimization and Applications
Authors: , ,
Keywords: programming: convex
Abstract:

In this paper, we consider convex optimization problems with cone constraints (CPC in short). We study generalized weak sharp minima properties for (CPC) in the Banach space and Hilbert space settings, respectively. Some criteria and characterizations for the solution set to be a set of generalized weak sharp minima for (CPC) are derived. As an application, we propose an algorithm for (CPC) in the Hilbert space setting. Convergence analysis of this algorithm is given.

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