In this work we consider the crtical points of a vector-valued functions, as defined by S. Smale. We study their stability in order to obtain a necessary conditions for Pareto efficiency. We point out, by an example, that the classical notions of stability (concerning a single point) are not suitable in this setting. We use a stability notion for sets to prove that the counterimage of a minimal point is stable. This result is based on the study of a dynamical system defined by a differential inclusion. In the vector case this inclusion plays the same role as gradient system in the scalar setting.
|Numero di pagine||10|
|Rivista||JOURNAL OF INFORMATION & OPTIMIZATION SCIENCES|
|Stato di pubblicazione||Pubblicato - 2003|
- critical points
- vector-valued function