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This paper concerns a fractional function of the form xTalpha/radicxTBx, where B is positive definite. We consider the game of choosing x from a convex set, to maximize the function, and choosing (alpha, B) from a convex set, to minimize it. We prove the existence of a saddle point and describe an efficient method, based on convex optimization, for computing it. We describe applications in machine learning (robust Fisher linear discriminant analysis), signal processing (robust beam- forming, robust matched filtering), and finance (robust portfolio selection). In these applications, x corresponds to some design variables to be chosen, and the pair (alpha, B) corresponds to the statistical model, which is uncertain.
Decision and Control, 2007 46th IEEE Conference on
Date of Conference: 12-14 Dec. 2007