Open question concerning generalized multi-source Weber problem

In this paper we consider the generalized Weber problem of m new facilities with respect to n regions in order to minimizing the sum of area produced by facilities and regions. We assumed that each region is a nonempty convex closed bounded subset of 2 R . We state an algorithm for solving this problem which is consists of a location phase and an allocation phase in each iteration. We will present an idea that its correction introduce as an open question.

Keywords:

variational inequality , location-allocation , global convergence