<s>
Proximal	B-Algorithm
gradient	I-Algorithm
methods	I-Algorithm
are	O
a	O
generalized	O
form	O
of	O
projection	B-Algorithm
used	O
to	O
solve	O
non-differentiable	O
convex	O
optimization	O
problems	O
.	O
</s>
<s>
The	O
lack	O
of	O
differentiability	O
rules	O
out	O
conventional	O
smooth	O
optimization	O
techniques	O
like	O
the	O
steepest	B-Algorithm
descent	I-Algorithm
method	I-Algorithm
and	O
the	O
conjugate	B-Algorithm
gradient	I-Algorithm
method	I-Algorithm
,	O
but	O
proximal	B-Algorithm
gradient	I-Algorithm
methods	I-Algorithm
can	O
be	O
used	O
instead	O
.	O
</s>
<s>
Proximal	B-Algorithm
gradient	I-Algorithm
methods	I-Algorithm
starts	O
by	O
a	O
splitting	O
step	O
,	O
in	O
which	O
the	O
functions	O
are	O
used	O
individually	O
so	O
as	O
to	O
yield	O
an	O
easily	O
implementable	O
algorithm	O
.	O
</s>
<s>
split	O
Bregman	B-Algorithm
are	O
special	O
instances	O
of	O
proximal	O
algorithms	O
.	O
</s>
<s>
For	O
the	O
theory	O
of	O
proximal	B-Algorithm
gradient	I-Algorithm
methods	I-Algorithm
from	O
the	O
perspective	O
of	O
and	O
with	O
applications	O
to	O
statistical	B-General_Concept
learning	I-General_Concept
theory	I-General_Concept
,	O
see	O
proximal	B-Algorithm
gradient	I-Algorithm
methods	I-Algorithm
for	I-Algorithm
learning	I-Algorithm
.	O
</s>
<s>
One	O
of	O
the	O
widely	O
used	O
convex	O
optimization	O
algorithms	O
is	O
projections	B-Algorithm
onto	O
convex	O
sets	O
(	O
POCS	O
)	O
.	O
</s>
<s>
In	O
POCS	O
method	O
each	O
set	O
is	O
incorporated	O
by	O
its	O
projection	B-Algorithm
operator	I-Algorithm
.	O
</s>
<s>
However	O
beyond	O
such	O
problems	O
projection	B-Algorithm
operators	I-Algorithm
are	O
not	O
appropriate	O
and	O
more	O
general	O
operators	O
are	O
required	O
to	O
tackle	O
them	O
.	O
</s>
<s>
Among	O
the	O
various	O
generalizations	O
of	O
the	O
notion	O
of	O
a	O
convex	O
projection	B-Algorithm
operator	I-Algorithm
that	O
exist	O
,	O
proximity	O
operators	O
are	O
best	O
suited	O
for	O
other	O
purposes	O
.	O
</s>
