English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The Weber problem consists of finding a point in $\mathbbm{R}^n$ thatminimizes the weighted sum of distances from $m$ points in $\mathbbm{R}^n$ thatare not collinear. An application that motivated this problem is the optimallocation of facilities in the 2-dimensional case. A classical method to solvethe Weber problem, proposed by Weiszfeld in 1937, is based on a fixed pointiteration.  In this work a Weber problem constrained to a closed and convex set isconsidered. A Weiszfeld-like algorithm, well defined even when an iterate is avertex, is presented. The iteration function $Q$ that defines the proposedalgorithm, is based mainly on an orthogonal projection over the feasible set,combined with the iteration function of a modified Weiszfeld algorithmpresented by Vardi and Zhang in 2001.  It can be seen that the proposed algorithm generates a sequence of feasibleiterates that have descent properties. Under certain hypotheses, the limit ofthis sequence satisfies the KKT optimality conditions, is a fixed point of theiteration function that defines the algorithm, and is the solution of theconstrained minimization problem. Numerical experiments confirmed thetheoretical results.

A Weiszfeld-like algorithm for a Weber location problem constrained to a closed and convex set