A Partial Regularization Method for Saddle Point Seeking

This article generalizes the Nash equilibrium approach to linear programming to the saddle point problem. The problem is shown to be equivalent to a non-zero sum game in which objectives of the players are obtained by partial regularization of the original function. Based on that, a solution method is developed in which the players improve their decisions while anticipating the steps of their opponents. Strong convergence of the method is proved and application to convex optimization is discussed. Note: This document is not complete since some graphics were generated manually and are therefore not included in the online version. For the complete document contact IIASA's Publications department.