Bounded homotopy path approach to the solution of linear complementarity problems

A. Dutta () and A. K. Das ()
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A. Dutta: ITER Siksha O Anusandhan
A. K. Das: Indian Statistical Institute

OPSEARCH, 2024, vol. 61, issue 1, No 17, 352-372

Abstract: Abstract In this article a bounded path approach is introduced to find the solution of linear complementarity problem. The interior point method for linear programming was a kind of path-following method. The difficulty of finding a strictly feasible initial point for the interior point algorithm can be replaced appropriately by combining the interior point with homotopy method. A new homotopy function as well as a new approach are proposed to trace a homotopy path to find the solution of linear complementarity problem with various matrix classes. It is shown that the homotopy path approaching to the solution is smooth and bounded. Various classes of numerical examples are illustrated to show the effectiveness of the proposed algorithm.

Keywords: Linear complementarity problem; Homotopy method; Interior point method; Strictly feasible point; 90C33; 15A39; 15B99 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s12597-023-00687-4

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