Exact Line Search Method for Solving Nonsymmetric Algebraic Riccati Equations Arising from Open-loop Linear Quadratic Differential Games

We consider a set of coupled algebraic Riccati equations arising from noncooperative open-loop linear quadratic differential games for infinite-planning horizon and two-player case. Such coupled algebraic Riccati equations can be rewritten as a nonsymmetric algebraic Riccati equation. In this paper, we will discuss exact line search method for solving nonsymmetric algebraic Riccati equations. This method is a modification of Newton's method. We give numerical examples and compare the results with Newton's method and fixed point iteration to show the effectiveness of exact line search method in a special case.