  An optimization problem has been formulated to find a resonant current
extremizing various antenna parameters. The method is presented on, but not
limited to, particular cases of gain $G$, quality factor $Q$, gain to quality
factor ratio $G/Q$, and radiation efficiency $\eta$ of canonical shapes with
conduction losses explicitly included. The Rao-Wilton-Glisson basis
representation is used to simplify the underlying algebra while still allowing
surface current regions of arbitrary shape to be treated. By switching to
another basis generated by a specific eigenvalue problem, it is finally shown
that the optimal current can, in principle, be found as a combination of a few
eigenmodes. The presented method constitutes a general framework in which the
antenna parameters, expressed as bilinear forms, can automatically be
extremized.
