Subdifferentials of Distance Functions and Applications to Facility Location Problems

Authors

Juan Salinas Jr., University of Texas-Pan American

Date of Award

8-2011

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Dr. Mau Nam Nguyen

Second Advisor

Dr. Barnabas Bede

Third Advisor

Dr. Paul Bracken

Abstract

The classical Heron problem states: on a given straight line in the plane, find a point C such that the sum of the distances from C to the given points A and B is minimal. This problem can be solved using standard geometry or differential calculus. In the light of modern convex analysis, we are able to investigate more general versions of this problem. In this thesis we propose and solve the following problem: on a given nonempty closed convex subset of IRs , find a point such that the sum of the distances from that point to n given nonempty closed convex subsets of IRs is minimal.

Comments

Copyright 2011 Juan Salinas Jr. All Rights Reserved.

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Granting Institution

University of Texas-Pan American