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

Fabio Vitor () and Todd Easton ()
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Fabio Vitor: University of Nebraska at Omaha
Todd Easton: The University of Utah

Computational Optimization and Applications, 2022, vol. 83, issue 1, No 7, 246 pages

Abstract: 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%.

Keywords: Linear programming; Interior point methods; Two-dimensional search algorithms; Multidimensional searches; Search directions; 90C05; 90C51 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10589-022-00385-9

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