<s>
In	O
mathematical	O
optimization	O
,	O
the	O
problem	O
of	O
non-negative	B-Algorithm
least	I-Algorithm
squares	I-Algorithm
(	O
NNLS	O
)	O
is	O
a	O
type	O
of	O
constrained	B-Algorithm
least	I-Algorithm
squares	I-Algorithm
problem	O
where	O
the	O
coefficients	O
are	O
not	O
allowed	O
to	O
become	O
negative	O
.	O
</s>
<s>
Non-negative	B-Algorithm
least	I-Algorithm
squares	I-Algorithm
problems	O
turn	O
up	O
as	O
subproblems	O
in	O
matrix	O
decomposition	O
,	O
e.g.	O
</s>
<s>
This	O
problem	O
is	O
convex	O
,	O
as	O
is	O
positive	B-Algorithm
semidefinite	I-Algorithm
and	O
the	O
non-negativity	O
constraints	O
form	O
a	O
convex	O
feasible	O
set	O
.	O
</s>
<s>
The	O
first	O
widely	O
used	O
algorithm	O
for	O
solving	O
this	O
problem	O
is	O
an	O
active-set	B-Algorithm
method	I-Algorithm
published	O
by	O
Lawson	O
and	O
Hanson	O
in	O
their	O
1974	O
book	O
Solving	O
Least	O
Squares	O
Problems	O
.	O
</s>
<s>
In	O
pseudocode	B-Language
,	O
this	O
algorithm	O
looks	O
as	O
follows	O
:	O
</s>
<s>
Variants	O
of	O
this	O
algorithm	O
are	O
available	O
in	O
MATLAB	B-Language
as	O
the	O
routine	O
and	O
in	O
SciPy	B-Application
as	O
.	O
</s>
<s>
Other	O
algorithms	O
include	O
variants	O
of	O
Landweber	B-Algorithm
's	O
gradient	B-Algorithm
descent	I-Algorithm
method	I-Algorithm
and	O
coordinate-wise	B-Algorithm
optimization	I-Algorithm
based	O
on	O
the	O
quadratic	B-Algorithm
programming	I-Algorithm
problem	O
above	O
.	O
</s>
