Accelerated ADMM Algorithm For Solving Games Theory with Mixed Strategies

Abstract

This study presents the Alternating Direction Method of multipliers (ADMM) for solving linear programming problem (LPP) which is also known as proximal point algorithm. The ADMM was deployed because of its strong convergence properties of the method of multipliers, the decomposibility property of dual ascent and the potential to solve large- scale structured optimization problems. The update formulas for the LPP were derived from the associated augmented Lagrangian with the primal and dual residuals also derived for the convergence of the algorithm. The Game theory was re-structured into a LPP amenable to the ADMM with a derived matrix operator that is invertible to guarantee its convergence.  Numerical examples were simulated to ascertain the perfoemace of the method in terms of speed and accuray.

AMS subject classifications: 49, 65, 90