Theoretical convergence of large-step primal-dual interior point algorithms for linear programming

This paper proposes two sets of rules Rule G and Rule P for controlling step lengths in a generic primal dual interior point method for solving the linear program ming problem in standard form and its dual Theoretically Rule G ensures the global convergence while Rule P which is a special case of Rule G ensures the O nL iteration polynomial time computational complexity Both rules depend only on the lengths of the steps from the current iterates in the primal and dual spaces to the respective boundaries of the primal and dual feasible regions They rely neither on neighborhoods of the central trajectory nor on potential function These rules allow large steps without performing any line search Rule G is especially exible enough for implementation in practically e cient primal dual interior point algorithms