This paper presents a method for finding an Lqclosest-point to a set of affine subspaces, that is a point for which the sum of the q-th power of orthogonal distances to all the subspaces is minimized, where 1 ≤ q < 2. We give a theoretical proof for the convergence of the proposed algorithm to a unique Lq minimum. The proposed method is motivated by the Lq Weiszfeld algorithm, an extremely simp...

We present a new iterative method for probabilistic clustering of data. Given clusters, their centers and the distances of data points from these centers, the probability of cluster membership at any point is assumed inversely proportional to the distance from (the center of) the cluster in question. This assumption is our working principle. The method is a generalization, to several centers, o...

In this paper we introduce a new facility location model, called backup multifacility location problem by considering the ideal radius for each customer. In this problem the location of clients are given in the plane. A radius is assigned to each client. We should find the location of new facilities, which some of them may fail with a given probability, such that the sum of weighted distances f...

Location theory is an interstice field of optimization and operations research‎. ‎In the classic location models‎, ‎the goal is finding the location of one or more facilities such that some criteria such as transportation cost‎, ‎the sum of distances passed by clients‎, ‎total service time, and cost of servicing are minimized‎. ‎The goal Weber location problem is a special case of location mode...

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 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 ...

differential transform method has been applied to solve many functional equations so far. in this article, we have used this method to solve wave-like equations. differential transform method is capable of reducing the size of computational work. exact solutions can also be achieved by the known forms of the series solutions. some examples are prepared to show theefficiency and simplicity of th...