On Differentiability of Metric Projections onto Moving Convex Sets

نویسنده

  • Darinka Dentcheva
چکیده

We consider properties of the metric projections onto moving convex sets in normed linear spaces. Under certain conditions about the norm, directional diierentiability (of higher order) of the metric projections at boundary points is characterized. The characterization is formulated in terms diierentiability of multifunctions and properties of the set-derivatives are shown.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Existence and Differentiability of Metric Projections in Hilbert Spaces

This paper considers metric projections onto a closed subset S of a Hilbert space. If the set S is convex, then it is well known that the corresponding metric projections always exist, unique and directionally differentiable at boundary points of S. These properties of metric projections are considered for possibly nonconvex sets S. In particular, existence and directional differentiability of ...

متن کامل

Differentiability Properties of Metric Projections onto Convex Sets

It is known that directional differentiability of metric projection onto a closed convex set in a finite dimensional space is not guaranteed. In this paper we discuss sufficient conditions ensuring directional differentiability of such metric projections. The approach is based on a general theory of sensitivity analysis of parameterized optimization problems.

متن کامل

Differentiability of themetric projection onto a convex set with singular boundary points

The differentiability of the metric projection P onto a closed convex set K in Rn is examined. The boundary ãK can have singular points of orders k ̈ −1Ù 0Ù 1ÜÙ n − 1. Here k ̈ −1 corresponds to the interior points of K , k ̈ 0 to regular points of the boundary (i.e., faces), k ̈ 1ÙÜ Ù n − 2 to edges and k ̈ n − 1 to vertices. It is assumed that for every k the set of all singular points forms ...

متن کامل

Convexity and Geodesic Metric Spaces

In this paper, we first present a preliminary study on metric segments and geodesics in metric spaces. Then we recall the concept of d-convexity of sets and functions in the sense of Menger and study some properties of d-convex sets and d-convex functions as well as extreme points and faces of d-convex sets in normed spaces. Finally we study the continuity of d-convex functions in geodesic metr...

متن کامل

Removal of compression artifacts using projections onto convex sets and line process modeling

We present a new image recovery algorithm to remove, in addition to blocking, ringing artifacts from compressed images and video. This new algorithm is based on the theory of projections onto convex sets (POCS). A new family of directional smoothness constraint sets is defined based on line processes modeling of the image edge structure. The definition of these smoothness sets also takes into a...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • Annals OR

دوره 101  شماره 

صفحات  -

تاریخ انتشار 2001