<s>
Sequential	B-Algorithm
linear-quadratic	I-Algorithm
programming	I-Algorithm
(	O
SLQP	B-Algorithm
)	O
is	O
an	O
iterative	B-Algorithm
method	I-Algorithm
for	O
nonlinear	B-Algorithm
optimization	I-Algorithm
problems	I-Algorithm
where	O
objective	O
function	O
and	O
constraints	O
are	O
twice	O
continuously	O
differentiable	O
.	O
</s>
<s>
Similarly	O
to	O
sequential	B-Algorithm
quadratic	I-Algorithm
programming	I-Algorithm
(	O
SQP	O
)	O
,	O
SLQP	B-Algorithm
proceeds	O
by	O
solving	O
a	O
sequence	O
of	O
optimization	O
subproblems	O
.	O
</s>
<s>
This	O
decomposition	O
makes	O
SLQP	B-Algorithm
suitable	O
to	O
large-scale	O
optimization	O
problems	O
,	O
for	O
which	O
efficient	O
LP	O
and	O
EQP	O
solvers	O
are	O
available	O
,	O
these	O
problems	O
being	O
easier	O
to	O
scale	O
than	O
full-fledged	O
quadratic	B-Algorithm
programs	I-Algorithm
.	O
</s>
<s>
Consider	O
a	O
nonlinear	B-Algorithm
programming	I-Algorithm
problem	O
of	O
the	O
form	O
:	O
</s>
<s>
In	O
the	O
LP	O
phase	O
of	O
SLQP	B-Algorithm
,	O
the	O
following	O
linear	B-Algorithm
program	I-Algorithm
is	O
solved	O
:	O
</s>
<s>
Let	O
denote	O
the	O
active	B-Algorithm
set	I-Algorithm
at	O
the	O
optimum	O
of	O
this	O
problem	O
,	O
that	O
is	O
to	O
say	O
,	O
the	O
set	O
of	O
constraints	O
that	O
are	O
equal	O
to	O
zero	O
at	O
.	O
</s>
<s>
In	O
the	O
EQP	O
phase	O
of	O
SLQP	B-Algorithm
,	O
the	O
search	O
direction	O
of	O
the	O
step	O
is	O
obtained	O
by	O
solving	O
the	O
following	O
equality-constrained	O
quadratic	B-Algorithm
program	I-Algorithm
:	O
</s>
