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

Authors:
S. Huang;K. O. Kortanek
Affiliations:
Department of Management Sciences, The University of Iowa, Iowa City, IA 52242, USA;Department of Management Sciences, The University of Iowa, Iowa City, IA 52242, USA
Venue:
Operations Research Letters
Year:
1991

Citing 6
Cited 0

A new polynomial-time algorithm for linear programming

Combinatorica
A primal-dual interior point algorithm for linear programming

on Progress in Mathematical Programming: Interior-Point and Related Methods
A polynomial-time primal-dual affine scaling algorithm for linear and convex quadratic programming and its power series extension

Mathematics of Operations Research
A centered projective algorithm for linear programming

Mathematics of Operations Research
An OnL iteration potential reduction algorithm for linear complementary problems

Mathematical Programming: Series A and B
An OL(n3) potential reduction algorithm for linear programming

Mathematical Programming: Series A and B

Quantified Score

Hi-index	0.00

Visualization

Abstract

Potential function reduction algorithms for linear programming and the linear complementarity problem use key projections p"x and p"s which are derived from the 'double' potential function, @f(x, s) = o ln(x^Ts)-@S"j" "=" "1^n ln(x"js"j), where x and s are primal and dual slacks vectors. For non-symmetric LP duality we show that the existence of s, y, xsatisfyings = c - A^Ty, Ax = b such that p"x = (@r/x^Ts) Xs - e and p"s = (@r/x^Ts)Sx - e yields simultaneous primal and dual projection-based updating during the process of reducing the potential function o. The role of x, sin an O(@/nL) simultaneous primal-dual update algorithm is discussed.