Critical points index for vector functions and vector optimization

被引:7
作者
Miglierina, E. [1 ]
Molho, E. [2 ]
Rocca, M. [1 ]
机构
[1] Univ Insubria, Dept Econ, I-21100 Varese, Italy
[2] Univ Pavia, Dept Management Sci, I-27100 Pavia, Italy
关键词
vector optimization; critical points; Morse index; second-order differentials;
D O I
10.1007/s10957-008-9383-5
中图分类号
C93 [管理学]; O22 [运筹学];
学科分类号
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要
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.
引用
收藏
页码:479 / 496
页数:18
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