# Minimizing sequence

From Encyclopedia of Mathematics

A sequence of elements from a set for which the corresponding sequence of function values tends to the greatest lower bound of on , that is,

The compactness of a minimizing sequence, that is, the existence of a subsequence converging to an element of , in combination with the lower semi-continuity of , guarantees the existence of an optimal element

In approximation theory, a minimizing sequence for a given element of a metric space is a sequence for which

**How to Cite This Entry:**

Minimizing sequence.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Minimizing_sequence&oldid=11597

This article was adapted from an original article by Yu.N. Subbotin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article