<s>
A	O
signomial	B-Algorithm
is	O
an	O
algebraic	O
function	O
of	O
one	O
or	O
more	O
independent	O
variables	O
.	O
</s>
<s>
Signomials	B-Algorithm
are	O
closed	O
under	O
addition	O
,	O
subtraction	O
,	O
multiplication	O
,	O
and	O
scaling	O
.	O
</s>
<s>
If	O
we	O
restrict	O
all	O
to	O
be	O
positive	O
,	O
then	O
the	O
function	O
f	O
is	O
a	O
posynomial	B-Algorithm
.	O
</s>
<s>
Consequently	O
,	O
each	O
signomial	B-Algorithm
is	O
either	O
a	O
posynomial	B-Algorithm
,	O
the	O
negative	O
of	O
a	O
posynomial	B-Algorithm
,	O
or	O
the	O
difference	O
of	O
two	O
posynomials	B-Algorithm
.	O
</s>
<s>
If	O
,	O
in	O
addition	O
,	O
all	O
exponents	O
are	O
non-negative	O
integers	O
,	O
then	O
the	O
signomial	B-Algorithm
becomes	O
a	O
polynomial	O
whose	O
domain	O
is	O
the	O
positive	O
orthant	O
.	O
</s>
<s>
is	O
a	O
signomial	B-Algorithm
.	O
</s>
<s>
The	O
term	O
"	O
signomial	B-Algorithm
"	O
was	O
introduced	O
by	O
Richard	O
J	O
.	O
Duffin	O
and	O
Elmor	O
L	O
.	O
Peterson	O
in	O
their	O
seminal	O
joint	O
work	O
on	O
general	O
algebraic	O
optimization	O
—	O
published	O
in	O
the	O
late	O
1960s	O
and	O
early	O
1970s	O
.	O
</s>
<s>
Nonlinear	B-Algorithm
optimization	I-Algorithm
problems	O
with	O
constraints	B-Application
and/or	O
objectives	O
defined	O
by	O
signomials	B-Algorithm
are	O
harder	O
to	O
solve	O
than	O
those	O
defined	O
by	O
only	O
posynomials	B-Algorithm
,	O
because	O
(	O
unlike	O
posynomials	B-Algorithm
)	O
signomials	B-Algorithm
cannot	O
necessarily	O
be	O
made	O
convex	O
by	O
applying	O
a	O
logarithmic	O
change	O
of	O
variables	O
.	O
</s>
<s>
Nevertheless	O
,	O
signomial	B-Algorithm
optimization	O
problems	O
often	O
provide	O
a	O
much	O
more	O
accurate	O
mathematical	O
representation	O
of	O
real-world	O
nonlinear	B-Algorithm
optimization	I-Algorithm
problems	O
.	O
</s>
