Constrained Optimization Using Geometric Algebra and its Application to Signal Analysis

Abstract

In this paper we discuss a mathematical system based on the algebras of Grassmann and Clifford [4, 1], called geometric algebra [6]. It is shown how geometric algebra can be used to carry out, in a simple manner, various complex manipulations relevant to matrix-based problems, including that of optimization. In particular we look at how differentiation of certain matrix functions with respect to the matrix, can easily be achieved. The encoding of structure into such problems will be discussed and applied to a multi-source signal separation problem. Other applications are also discussed.