<s>
In	O
applied	O
mathematics	O
,	O
weak	B-Algorithm
duality	I-Algorithm
is	O
a	O
concept	O
in	O
optimization	O
which	O
states	O
that	O
the	O
duality	B-Algorithm
gap	I-Algorithm
is	O
always	O
greater	O
than	O
or	O
equal	O
to	O
0	O
.	O
</s>
<s>
That	O
means	O
the	O
solution	O
to	O
the	O
dual	O
(	O
minimization	O
)	O
problem	O
is	O
always	O
greater	O
than	O
or	O
equal	O
to	O
the	O
solution	O
to	O
an	O
associated	O
primal	B-Algorithm
problem	I-Algorithm
.	O
</s>
<s>
This	O
is	O
opposed	O
to	O
strong	B-Algorithm
duality	I-Algorithm
which	O
only	O
holds	O
in	O
certain	O
cases	O
.	O
</s>
<s>
Many	O
primal-dual	O
approximation	B-Algorithm
algorithms	I-Algorithm
are	O
based	O
on	O
the	O
principle	O
of	O
weak	B-Algorithm
duality	I-Algorithm
.	O
</s>
<s>
The	O
primal	B-Algorithm
problem	I-Algorithm
:	O
</s>
<s>
The	O
weak	B-Algorithm
duality	I-Algorithm
theorem	O
states	O
.	O
</s>
<s>
More	O
generally	O
,	O
if	O
is	O
a	O
feasible	O
solution	O
for	O
the	O
primal	O
maximization	O
problem	O
and	O
is	O
a	O
feasible	O
solution	O
for	O
the	O
dual	O
minimization	O
problem	O
,	O
then	O
weak	B-Algorithm
duality	I-Algorithm
implies	O
where	O
and	O
are	O
the	O
objective	O
functions	O
for	O
the	O
primal	O
and	O
dual	O
problems	O
respectively	O
.	O
</s>
