ON LOCAL PARETO OPTIMA OF REAL ANALYTIC MAPPINGS

Ha Huy Vui and Pham Tien Son

Abstract

           This paper deals with the local problem of optimizing several analytic functions at the same time. We
prove that the Milnor number of an isolated complete intersection singularity at a local Pareto optimal point is odd. Furthermore, high-order necessary and almost sufficient conditions are given, allowing one to recognize from the Newton diagram of an analytic mapping at the origin whether this point is a local Pareto optimum.