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 controll ing step lengths in a generic primal-dual interior point method for so lving the linear programming problem in standard form and its dual. Th eoretically, Rule G ensures the global convergence, while Rule P, whic h is a special case of Rule G, ensures the O(nL) iteration polynomial- time computational complexity. Both rules depend only on the lengths o f the steps from the current iterates in the primal and dual spaces to the respective boundaries of the primal and dual feasible regions. Th ey rely neither on neighborhoods of the central trajectory nor on pote ntial function. These rules allow large steps without performing any l ine search. Rule G is especially flexible enough for implementation in practically efficient primal-dual interior point algorithms.