Complexity of Interior Point Methods for a Class of Linear Complementarity Problems Using a Kernel Function with Trigonometric Growth Term

Sajad Fathi-Hafshejani (), Alireza Fakharzadeh Jahromi, Mohammad Reza Peyghami and Shengyuan Chen
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Sajad Fathi-Hafshejani: Shiraz University of Technology
Alireza Fakharzadeh Jahromi: Shiraz University of Technology
Mohammad Reza Peyghami: K. N. Toosi University of Technology
Shengyuan Chen: York University

Journal of Optimization Theory and Applications, 2018, vol. 178, issue 3, No 11, 935-949

Abstract: Abstract In this paper, we propose a large-update primal-dual interior point method for solving a class of linear complementarity problems based on a new kernel function. The main aspects distinguishing our proposed kernel function from the others are as follows: Firstly, it incorporates a specific trigonometric function in its growth term, and secondly, the corresponding barrier term takes finite values at the boundary of the feasible region. We show that, by resorting to relatively simple techniques, the primal-dual interior point methods designed for a specific class of linear complementarity problems enjoy the so-called best-known iteration complexity for the large-update methods.

Keywords: Kernel function; Large-update methods; Linear complementarity problem; Primal-dual interior point methods; 90C33; 90C51 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10957-018-1344-z

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