<s>
In	O
applied	O
mathematics	O
and	O
computer	B-General_Concept
science	I-General_Concept
,	O
variable	B-Algorithm
splitting	I-Algorithm
is	O
a	O
decomposition	O
method	O
that	O
relaxes	O
a	O
set	O
of	O
constraints	O
.	O
</s>
<s>
This	O
new	O
linking	O
constraint	B-Application
can	O
be	O
relaxed	O
with	O
a	O
Lagrange	O
multiplier	O
;	O
in	O
many	O
applications	O
,	O
a	O
Lagrange	O
multiplier	O
can	O
be	O
interpreted	O
as	O
the	O
price	O
of	O
equality	O
between	O
x1	O
and	O
x2	O
in	O
the	O
new	O
constraint	B-Application
.	O
</s>
<s>
A	O
solution	O
to	O
the	O
relaxed	O
problem	O
(	O
with	O
variable	B-Algorithm
splitting	I-Algorithm
)	O
provides	O
an	O
approximate	O
solution	O
to	O
the	O
original	O
problem	O
:	O
further	O
,	O
the	O
approximate	O
solution	O
to	O
the	O
relaxed	O
problem	O
provides	O
a	O
"	O
warm	O
start	O
"	O
,	O
a	O
good	O
initialization	O
of	O
an	O
iterative	O
method	O
for	O
solving	O
the	O
original	O
problem	O
(	O
having	O
only	O
the	O
x	O
variable	O
)	O
.	O
</s>
