A Minimax Theorem with Applications to Machine Learning, Signal Processing, and Finance
S.-J. Kim and S. Boyd
SIAM Journal on Optimization, 19(3):1344–1367, November 2008.
This paper concerns a fractional function of the form , where is positive definite. We consider the game of choosing from a convex set, to maximize the function, and choosing 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 beamforming, robust matched filtering), and finance (robust portfolio selection). In these applications, corresponds to some design variables to be chosen, and the pair corresponds to the statistical model, which is uncertain.