标题： 变分分析在广义海龙问题中的应用 显示英文标题

标题： Applications of Variational Analysis to a Generalized Heron Problem

摘要： 本文是我们利用变分分析和广义微分的先进工具解决若干几何问题及其扩展的延续工作。这里我们从定性和数值的角度提出并研究了如下最优位置问题及其进一步扩展：在一个巴拿赫空间的非空子集上，寻找一点，使得它到该空间中给定的$n$个非空子集的距离之和最小。 这是经典海伦问题的一个推广版本：在一条给定直线上，寻找一点 C，使得它到给定两点 A 和 B 的距离之和最小。 我们证明，先进的变分技术使我们在某些重要的情形下能够完全解决这类最优位置问题。 显示英文摘要

摘要： This paper is a continuation of our ongoing efforts to solve a number of geometric problems and their extensions by using advanced tools of variational analysis and generalized differentiation. Here we propose and study, from both qualitative and numerical viewpoints, the following optimal location problem as well as its further extensions: on a given nonempty subset of a Banach space, find a point such that the sum of the distances from it to $n$ given nonempty subsets of this space is minimal. This is a generalized version of the classical Heron problem: on a given straight line, find a point C such that the sum of the distances from C to the given points A and B is minimal. We show that the advanced variational techniques allow us to completely solve optimal location problems of this type in some important settings.