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A modified projection method for linear feasibility problems

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Abstract

In this paper, we present a modified projection method for the linear feasibility problems (LFP). Compared with the existing methods, the new method adopts a surrogate technique to obtain new iteration instead of the line search procedure with fixed stepsize. For the new method, we first show its global convergence under the condition that the solution set is nonempty, and then establish its linear convergence rate. Preliminary numerical experiments show that this method has good performance.

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Authors and Affiliations

  1. School of Operations Research and Management Science, Qufu Normal University, Rizhao, 276800, PRC

    Yi-Ju Wang & Hong-Yu Zhang

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  1. Yi-Ju Wang
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  2. Hong-Yu Zhang
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Correspondence to Yi-Ju Wang.

Additional information

This work was supported by National Natural Science Foundation of China (No. 10771120) and Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.

Yi-Ju Wang received his B. Sc. and M. Sc. degrees in mathematics, and operations and cybernetics from Qufu Normal University, PRC in 1990 and 1993, respectively, and the Ph.D. degree in operations and cybernetics from the Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, PRC in 2001. He is currently a professor at Qufu Normal University.

His research interests include optimization theory and its applications.

Hong-Yu Zhang is a postgraduate student at Qufu Normal University, PRC.

His research interest includes nonlinear optimization.

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Wang, YJ., Zhang, HY. A modified projection method for linear feasibility problems. Int. J. Autom. Comput. 6, 401–405 (2009). https://doi.org/10.1007/s11633-009-0401-3

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  • DOI: https://doi.org/10.1007/s11633-009-0401-3

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