Further Developments in an Iterative Projection and Contraction Method for Linear Programming

Further Developments in an Iterative Projection and Contraction Method for Linear Programming

Year:    1993

Author:    Bing-Sheng He

Journal of Computational Mathematics, Vol. 11 (1993), Iss. 4 : pp. 350–364

Abstract

A linear programming problem can be translated into an equivalent general linear complementarity problem, which can be solved by an iterative projection and contraction (PC) method [6]. The PC method requires only two matrix-vector multiplications at each iteration and the efficiency in practice usually depends on the sparsity of the constraint-matrix. The prime PC algorithm in [6] is globally convergent; however, no statement can be made about the rate of convergence. Although a variant of the PC algorithm with constant step-size for linear programming [7] has a linear speed of convergence, it converges much slower in practice than the prime method [6]. In this paper, we develop a new step-size rule for the PC algorithm for linear programming such that the resulting algorithm is globally linearly convergent. We present some numerical experiments to indicate that it also works better in practice than the prime algorithm.  

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/1993-JCM-9334

Journal of Computational Mathematics, Vol. 11 (1993), Iss. 4 : pp. 350–364

Published online:    1993-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    15

Keywords:   

Author Details

Bing-Sheng He