NDLI: Applications of Variational Analysis to a Generalized Fermat-Torricelli Problem

Content Provider	Springer Nature Link
Author	Mordukhovich, Boris Nam, Nguyen Mau
Copyright Year	2010
Abstract	In this paper we develop new applications of variational analysis and generalized differentiation to the following optimization problem and its specifications: given n closed subsets of a Banach space, find such a point for which the sum of its distances to these sets is minimal. This problem can be viewed as an extension of the celebrated Fermat-Torricelli problem: given three points on the plane, find another point that minimizes the sum of its distances to the designated points. The generalized Fermat-Torricelli problem formulated and studied in this paper is of undoubted mathematical interest and is promising for various applications including those frequently arising in location science, optimal networks, etc. Based on advanced tools and recent results of variational analysis and generalized differentiation, we derive necessary as well as necessary and sufficient optimality conditions for the extended version of the Fermat-Torricelli problem under consideration, which allow us to completely solve it in some important settings. Furthermore, we develop and justify a numerical algorithm of the subgradient type to find optimal solutions in convex settings and provide its numerical implementations.
Starting Page	431
Ending Page	454
Page Count	24
File Format	PDF
ISSN	00223239
Journal	Journal of Optimization Theory and Applications
Volume Number	148
Issue Number	3
e-ISSN	15732878
Language	English
Publisher	Springer US
Publisher Date	2010-11-18
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Variational analysis and optimization Generalized Fermat-Torricelli problem Minimal time function Minkowski gauge Generalized differentiation Necessary and sufficient optimality conditions Subgradient-type algorithms Operations Research/Decision Theory Engineering Applications of Mathematics Theory of Computation Optimization Calculus of Variations and Optimal Control; Optimization
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Control and Optimization Management Science and Operations Research

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