<s>
Superiorization	B-Algorithm
is	O
an	O
iterative	B-Algorithm
method	I-Algorithm
for	O
constrained	B-Application
optimization	I-Application
.	O
</s>
<s>
It	O
is	O
used	O
for	O
improving	O
the	O
efficacy	O
of	O
an	O
iterative	B-Algorithm
method	I-Algorithm
whose	O
convergence	O
is	O
resilient	O
to	O
certain	O
kinds	O
of	O
perturbations	O
.	O
</s>
<s>
Such	O
perturbations	O
are	O
designed	O
to	O
"	O
force	O
"	O
the	O
perturbed	O
algorithm	O
to	O
produce	O
more	O
useful	O
results	O
for	O
the	O
intended	O
application	O
than	O
the	O
ones	O
that	O
are	O
produced	O
by	O
the	O
original	O
iterative	B-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
The	O
superiorization	B-Algorithm
methodology	O
is	O
very	O
general	O
and	O
has	O
been	O
used	O
successfully	O
in	O
many	O
important	O
practical	O
applications	O
,	O
such	O
as	O
iterative	B-Algorithm
reconstruction	I-Algorithm
of	O
images	O
from	O
their	O
projections	O
,	O
single-photon	O
emission	O
computed	O
tomography	O
,	O
radiation	O
therapy	O
and	O
nondestructive	O
testing	O
,	O
just	O
to	O
name	O
a	O
few	O
.	O
</s>
<s>
A	O
special	O
issue	O
of	O
the	O
journal	O
Inverse	O
Problems	O
is	O
devoted	O
to	O
superiorization	B-Algorithm
,	O
both	O
theory	O
and	O
applications	O
.	O
</s>
<s>
An	O
important	O
case	O
of	O
superiorization	B-Algorithm
is	O
when	O
the	O
original	O
algorithm	O
is	O
"	O
feasibility-seeking	O
"	O
(	O
in	O
the	O
sense	O
that	O
it	O
strives	O
to	O
find	O
some	O
point	O
in	O
a	O
feasible	O
region	O
that	O
is	O
compatible	O
with	O
a	O
family	O
of	O
constraints	O
)	O
and	O
the	O
perturbations	O
that	O
are	O
introduced	O
into	O
the	O
original	O
iterative	B-Algorithm
algorithm	I-Algorithm
aim	O
at	O
reducing	O
(	O
not	O
necessarily	O
minimizing	O
)	O
a	O
given	O
merit	O
function	O
.	O
</s>
<s>
In	O
this	O
case	O
,	O
superiorization	B-Algorithm
has	O
a	O
unique	O
place	O
in	O
optimization	O
theory	O
and	O
practice	O
.	O
</s>
<s>
Many	O
constrained	B-Application
optimization	I-Application
methods	O
are	O
based	O
on	O
methods	O
for	O
unconstrained	O
optimization	O
that	O
are	O
adapted	O
to	O
deal	O
with	O
constraints	O
.	O
</s>
<s>
Barrier	O
methods	O
or	O
penalty	B-Algorithm
methods	I-Algorithm
likewise	O
are	O
based	O
on	O
unconstrained	O
optimization	O
combined	O
with	O
various	O
"	O
add-on	O
"	O
s	O
that	O
guarantee	O
that	O
the	O
constraints	O
are	O
preserved	O
.	O
</s>
<s>
In	O
contrast	O
to	O
these	O
approaches	O
,	O
the	O
superiorization	B-Algorithm
methodology	O
can	O
be	O
viewed	O
as	O
an	O
antipodal	O
way	O
of	O
thinking	O
.	O
</s>
<s>
Furthermore	O
,	O
general-purpose	O
approaches	O
have	O
been	O
developed	O
for	O
automatically	O
superiorizing	O
iterative	B-Algorithm
algorithms	I-Algorithm
for	O
large	O
classes	O
of	O
constraints	O
sets	O
and	O
merit	O
functions	O
;	O
these	O
provide	O
algorithms	O
for	O
many	O
application	O
tasks	O
.	O
</s>
<s>
The	O
superiorization	B-Algorithm
methodology	O
and	O
perturbation	O
resilience	O
of	O
algorithms	O
are	O
reviewed	O
in	O
,	O
see	O
also	O
.	O
</s>
<s>
Current	O
work	O
on	O
superiorization	B-Algorithm
can	O
be	O
appreciated	O
from	O
a	O
continuously	O
updated	O
Internet	O
page	O
.	O
</s>
<s>
SNARK14	O
is	O
a	O
software	O
package	O
for	O
the	O
reconstruction	O
if	O
2D	O
images	O
from	O
1D	O
projections	O
that	O
has	O
a	O
built-in	O
capability	O
of	O
superiorizing	O
any	O
iterative	B-Algorithm
algorithm	I-Algorithm
for	O
any	O
merit	O
function	O
.	O
</s>
