Visible Points in Convex Sets and Best Approximation

TL;DR

This paper introduces the concept of visible points in convex sets, explores their properties, and demonstrates their usefulness in best approximation and potential applications in robotics.

Contribution

It defines and analyzes visible points in convex sets, linking this concept to best approximation and suggesting applications in robotics.

Findings

Visible points have specific basic properties within convex sets.

The concept aids in understanding and solving best approximation problems.

Potential applications in robotics are identified.

Abstract

The concept of a visible point of a convex set relative to a given point is introduced. A number of basic properties of such visible point sets is developed. In particular, it is shown that this concept is useful in the study of best approximation, and it also seems to have potential value in the study of robotics.