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=47850
Minimizing sequence. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Minimizing_sequence&oldid=47850
This article was adapted from an original article by Yu.N. Subbotin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article