Applying Metric Regularity to Compute a Condition Measure of a Smoothing Algorithm for Matrix Games
Boris S. Mordukhovich, Javier Peña, Vera Roshchina · SIAM Journal on Optimization · 2010
We develop an approach of variational analysis and generalized differentiation to conditioning issues for two-person zero-sum matrix games. Our major results establish precise relationships between a certain condition measure of the smoothing first-order algorithm proposed by Gilpin, Peña, and Sandholm [Proceedings of the 23rd Conference on Artificial Intelligence, 2008, pp. 75–82] and the exact bound of metric regularity for an associated set-valued mapping. In this way we compute the aforementioned condition measure in terms of the initial matrix game data.