  An optimization procedure for multi-transmitter (MISO) wireless power
transfer (WPT) systems based on tight semidefinite relaxation (SDR) is
presented. This method ensures physical realizability of MISO WPT systems
designed via convex optimization -- a robust, semi-analytical and intuitive
route to optimizing such systems. To that end, the nonconvex constraints
requiring that power is fed into rather than drawn from the system via all
transmitter ports are incorporated in a convex semidefinite relaxation, which
is efficiently and reliably solvable by dedicated algorithms. A test of the
solution then confirms that this modified problem is equivalent (tight
relaxation) to the original (nonconvex) one and that the true global optimum
has been found. This is a clear advantage over global optimization methods
(e.g. genetic algorithms), where convergence to the true global optimum cannot
be ensured or tested. Discussions of numerical results yielded by both the
closed-form expressions and the refined technique illustrate the importance and
practicability of the new method. It, is shown that this technique offers a
rigorous optimization framework for a broad range of current and emerging WPT
applications.
