<s>
Penalty	B-Algorithm
methods	I-Algorithm
are	O
a	O
certain	O
class	O
of	O
algorithms	O
for	O
solving	O
constrained	B-Application
optimization	I-Application
problems	I-Application
.	O
</s>
<s>
A	O
penalty	B-Algorithm
method	I-Algorithm
replaces	O
a	O
constrained	B-Application
optimization	I-Application
problem	I-Application
by	O
a	O
series	O
of	O
unconstrained	O
problems	O
whose	O
solutions	O
ideally	O
converge	O
to	O
the	O
solution	O
of	O
the	O
original	O
constrained	O
problem	O
.	O
</s>
<s>
The	O
unconstrained	O
problems	O
are	O
formed	O
by	O
adding	O
a	O
term	O
,	O
called	O
a	O
penalty	B-Algorithm
function	I-Algorithm
,	O
to	O
the	O
objective	O
function	O
that	O
consists	O
of	O
a	O
penalty	O
parameter	O
multiplied	O
by	O
a	O
measure	O
of	O
violation	O
of	O
the	O
constraints	O
.	O
</s>
<s>
In	O
the	O
above	O
equations	O
,	O
is	O
the	O
exterior	O
penalty	B-Algorithm
function	I-Algorithm
while	O
are	O
the	O
penalty	B-Algorithm
coefficients	I-Algorithm
.	O
</s>
<s>
In	O
each	O
iteration	O
k	O
of	O
the	O
method	O
,	O
we	O
increase	O
the	O
penalty	B-Algorithm
coefficient	I-Algorithm
(	O
e.g.	O
</s>
<s>
Image	B-General_Concept
compression	I-General_Concept
optimization	O
algorithms	O
can	O
make	O
use	O
of	O
penalty	B-Algorithm
functions	I-Algorithm
for	O
selecting	O
how	O
best	O
to	O
compress	O
zones	O
of	O
colour	O
to	O
single	O
representative	O
values	O
.	O
</s>
<s>
Barrier	B-Algorithm
methods	I-Algorithm
constitute	O
an	O
alternative	O
class	O
of	O
algorithms	O
for	O
constrained	B-Application
optimization	I-Application
.	O
</s>
