Elsevier

Operations Research Letters

Volume 10, Issue 9, December 1991, Pages 501-507
Operations Research Letters

A note on a potential reduction algorithm for LP with simultaneous primal-dual updating

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Abstract

Potential function reduction algorithms for linear programming and the linear complementarity problem use key projections px and ps which are derived from the ‘double’ potential function, φ(x, s) = ø ln(xTs)−Σj = 1n ln(xjsj), where x and s are primal and dual slacks vectors. For non-symmetric LP duality we show that the existence of s, y, x satisfying s = c − ATy, Ax = b such that px = (ϱ/xTs) Xs − e and ps = (ϱ/xTs)Sx − e yields simultaneous primal and dual projection-based updating during the process of reducing the potential function ø. The role of x, s in an O(√nL) simultaneous primal-dual update algorithm is discussed.

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