LINEAR-THETA METHOD FOR THE DISCRETIZATION AND NUMERICAL SOLUTION OF FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS WITH MULTIPLE RETARDATIONS

Abstract

This study presents a special case of proximal point algorithm for solving linear programming problem (LPP). This method, also known as the Alternating Direction Method of multipliers (ADMM), was deployed because of its strong convergence properties of the method of multipliers, the decomposability 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. Prisoner’s Dilemma in Game theory was tested with the ADMM provided the matrix operator is invertible to guarantee its convergence. Other Numerical examples were also tested and it was discovered that the developed algorithm performs faster than the conventional simplex method.