I
NSTANCE
:
Positive integer
n
, set of linear constraints, given as an
-matrix
A
and an
m
-vector
b
, specifying a
region
by
.
S
OLUTION
:
A multivariate polynomial
of total degree at most 2.
M
EASURE
:
The maximum value of
f
in the region specified by the linear constants,
i.e.,
.
Bad News:
Does not admit a
-approximation for any constant
[
42
].
Comment:
A
-approximation algorithm finds a solution that differs from the
optimal solution by at most the value
.
Variation in which we look for a polynomial
f
of any degree
does not admit a
-approximation for
for some
[
42
].
Note that these problems are known to be solvable in polynomial space but
are not known to be in NP.