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Projected orthogonal vectors in two-dimensional search interior point algorithms for linear programming

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Abstract

The vast majority of linear programming interior point algorithms successively move from an interior solution to an improved interior solution by following a single search direction, which corresponds to solving a one-dimensional subspace linear program at each iteration. On the other hand, two-dimensional search interior point algorithms select two search directions, and determine a new and improved interior solution by solving a two-dimensional subspace linear program at each step. This paper presents primal and dual two-dimensional search interior point algorithms derived from affine and logarithmic barrier search directions. Both search directions are determined by randomly partitioning the objective function into two orthogonal vectors. Computational experiments performed on benchmark instances demonstrate that these new methods improve the average CPU time by approximately 12% and the average number of iterations by 14%.

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Acknowledgements

This work was partially funded by the National Science Foundation (NSF) under the EPSCoR research program – Grant No. OIA-1557417. The authors also thank the anonymous referees for their valuable suggestions that improved the presentation of this paper.

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  1. Department of Mathematics, University of Nebraska at Omaha, Omaha, NE, 68182, USA

    Fabio Vitor

  2. Department of Mechanical Engineering, The University of Utah, Salt Lake City, UT, 84112, USA

    Todd Easton

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Vitor, F., Easton, T. Projected orthogonal vectors in two-dimensional search interior point algorithms for linear programming. Comput Optim Appl 83, 211–246 (2022). https://doi.org/10.1007/s10589-022-00385-9

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