  A memetic framework for optimal inverse design is proposed by combining a
local gradient-based procedure and a robust global scheme. The procedure is
based on method-of-moments matrices and does not demand full inversion of a
system matrix. Fundamental bounds are evaluated for all optimized metrics in
the same manner, providing natural stopping criteria and quality measures for
realized devices. Compared to density-based topology optimization, the proposed
routine does not require filtering or thresholding. Compared to commonly used
heuristics, the technique is significantly faster, still preserving a high
level of versatility and robustness. This is a two-part paper in which the
first part is devoted to the theoretical background and properties, and the
second part applies the method to examples of varying complexity.
