This is the first of a series of articles aimed at laying the foundations for construction of special purpose computing machinery for solving the proximity effect problem. In this article, we compare three different types of proximity correction approach (basic matrix inversion, gradient descent optimization, and optimization using a Shannon entropy regularizer). We show that entropy regularization does not result in physically unrealizable negative dose requests as does the matrix inversion and related methods, and always provides optimizations closer to target than those derived from "least-mean-square" type gradient descent. The implications of this approach for integrated co-processor design are outlined.