Minimizing sequence

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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

See Approximately-compact set.

How to Cite This Entry:
Minimizing sequence. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by Yu.N. Subbotin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article