Critical Points Index for Vector Functions and Vector Optimization |
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Authors: | E. Miglierina E. Molho M. Rocca |
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Affiliation: | (1) Department of Economics, University of Insubria, 21100 Varese, Italy;(2) Department of Management Sciences, University of Pavia, 27100 Pavia, Italy |
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Abstract: | In this work, we study the critical points of vector functions from ℝ n to ℝ m with n≥m, following the definition introduced by Smale in the context of vector optimization. The local monotonicity properties of a vector function around a critical point which are invariant with respect to local coordinate changes are considered. We propose a classification of critical points through the introduction of a generalized Morse index for a critical point, consisting of a triplet of nonnegative integers. The proposed index is based on the sign of an appropriate invariant vector-valued second-order differential. |
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Keywords: | Vector optimization Critical points Morse index Second-order differentials |
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