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Non-smooth projected primal-dual dynamical approach to solve the extended fermat-torricelli problem
R. Raveendran, , U. Vaidya
Published in Institute of Electrical and Electronics Engineers Inc.
Volume: 5
Issue: 3
Pages: 1109 - 1114
The problem of finding a point in Rn, from which the sum-of-distances to a finite number of non-empty, closed and convex sets is minimum is called generalized Fermat-Torricelli Problem (FTP). In applications, along with the point that minimizes sum-of-distances, it is important to know the points in the convex sets at which the minimum sum-of-distances is achieved. Various formulations existing in literature do not involve finding the optimal points in the convex sets. In this letter, we formulate a non-smooth convex optimization problem, with both the point/set of points which yields the minimum sum-of-distances as well as the corresponding points in the convex sets as primal variables. We term this problem as extended FTP (eFTP). We adopt non-smooth projected primal-dual dynamical approach to solve this problem. The proposed dynamical system can exhibit a continuum of equilibria. Hence we show semistability of the set of optimal points, which is the pertinent notion of stability for such systems. A distributed implementation of the primal-dual dynamical system is also presented in this letter. Four illustrative examples are considered for the simulation based validation of the solution proposed for eFTP. © 2017 IEEE.
About the journal
JournalData powered by TypesetIEEE Control Systems Letters
PublisherData powered by TypesetInstitute of Electrical and Electronics Engineers Inc.