The diff-convex (DC) problem of perturbed spatial median and the Weiszfeld algorithm in a framework for incomplete data is studied, and some level set theorems for general DC problems are provided. These results are then applied to study certain multiobjective formulations of clustering problems, and to yield a new algorithm for solving the multisource Weber problem.

The Fermat-Weber problem consists in finding a point in R that minimizes the weighted sum of distances from m points in R that are not collinear. An application that motivated this problem is the optimal location of industries in the 2-dimensional case. The Weber problem is a generalization of the well-known Fermat problem. An usual method to solve the Weber problem, proposed by Weiszfeld in 19...

In this paper we empirically analyze several algorithms for solving a Huff-like competitive location and design model for profit maximization in the plane. In particular, an exact interval branch-and-bound method and a multistart heuristic already proposed in the literature are compared with uego (Universal Evolutionary Global Optimizer), a recent evolutionary algorithm. Both the multistart heu...

In this paper we consider the problem of locating one new facility with respect to a given set of existing facilities in the plane and in the presence of convex polyhedral barriers. It is assumed that a barrier is a region where neither facility location nor travelling are permitted. The resulting nonconvex optimization problem can be reduced to a finite series of convex subproblems, which can ...

-The single facility minisum location problem requires finding a point in ~N that minimizes a sum of weighted distances to m given points. The distance measure is typically assumed in the literature to be either Euclidean or rectangular, or the more general Ip norm. Global convergence of a well-known iterative solution method named the Weiszfeld procedure has been proven under the proviso that ...

In this paper, we consider the continuous Fermat-Weber problem, where the customers are continuously (uniformly) distributed along the boundary of a convex polygon. We derive the closed-form expression for finding the average distance from a given point to the continuously distributed customers along the boundary. A Weiszfeld-type procedure is proposed for this model, which is shown to be linea...

The Fermat-Weber problem is one of the most widely studied problems in classical location theory. In his previous work, Brimberg (1995) attempts to resolve a conjecture posed by Chandrasekaran and Tamir (1989) on a convergence property of the Weiszfeld algorithm, a well-known iterative procedure used to solve this problem. More recently, C‹novas, MarÐn and Caflavate (2002) provide counterexampl...

In this paper, we define the geometric median of a probability measure on a Riemannian manifold, give its characterization and a natural condition to ensure its uniqueness. In order to calculate the median in practical cases, we also propose a subgradient algorithm and prove its convergence as well as estimating the error of approximation and the rate of convergence. The convergence property of...

Ensemble clustering is a recently evolving research direction in cluster analysis and has found several different application domains. In this work the complex ensemble clustering problem is reduced to the well-known Euclidean median problem by clustering embedding in vector spaces. The Euclidean median problem is solved by the Weiszfeld algorithm and an inverse transformation maps the Euclidea...