Newton-like methods for solving vector optimization problems |
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Authors: | Fang Lu |
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Affiliation: | College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China. |
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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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Keywords: | vector/multiobjective optimization critical point Newton-like method convergence scalarization |
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