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Applicable Analysis
An International Journal
Volume 93, 2014 - Issue 8
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Articles

Newton-like methods for solving vector optimization problems

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Pages 1567-1586 | Received 30 Apr 2013, Accepted 27 Aug 2013, Published online: 17 Sep 2013
 

Abstract

In the context of Euclidean spaces, we present an extension of the Newton-like method for solving vector optimization problems, with respect to the partial orders induced by a pointed, closed and convex cone with a nonempty interior. We study both exact and inexact versions of the Newton-like method. Under reasonable hypotheses, we prove stationarity of accumulation points of the sequences produced by Newton-like methods. Moreover, assuming strict cone-convexity of the objective map to the vector optimization problem, we establish convergence of the sequences to an efficient point whenever the initial point is in a compact level set.

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Acknowledgements

This research was partially supported by the National Natural Science Foundation of China (Grant number: 11301567) and the Fundamental Research Funds for the Central Universities (Grant number: CQDXWL-2012-010).

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