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A minimax theorem with applications to machine learning, signal processing, and finance

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2 Author(s)
Seung-Jean Kim ; Information Systems Laboratory Electrical Engineering Department, Stanford University, CA 94305-9510 USA ; Stephen Boyd

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.

Published in:

Decision and Control, 2007 46th IEEE Conference on

Date of Conference:

12-14 Dec. 2007