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