A Full-Newton Step Interior-Point Method for Monotone Weighted Linear Complementarity Problems

Soodabeh Asadi (), Zsolt Darvay (), Goran Lesaja (), Nezam Mahdavi-Amiri () and Florian Potra ()
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Soodabeh Asadi: Sharif University of Technology
Zsolt Darvay: Babeş-Bolyai University
Goran Lesaja: US Naval Academy
Nezam Mahdavi-Amiri: Sharif University of Technology
Florian Potra: University of Maryland

Journal of Optimization Theory and Applications, 2020, vol. 186, issue 3, No 7, 864-878

Abstract: Abstract In this paper, a full-Newton step Interior-Point Method for solving monotone Weighted Linear Complementarity Problem is designed and analyzed. This problem has been introduced recently as a generalization of the Linear Complementarity Problem with modified complementarity equation, where zero on the right-hand side is replaced with the nonnegative weight vector. With a zero weight vector, the problem reduces to a linear complementarity problem. The importance of Weighted Linear Complementarity Problem lies in the fact that it can be used for modelling a large class of problems from science, engineering and economics. Because the algorithm takes only full-Newton steps, the calculation of the step size is avoided. Under a suitable condition, the algorithm has a quadratic rate of convergence to the target point on the central path. The iteration bound for the algorithm coincides with the best iteration bound obtained for these types of problems.

Keywords: Weighted complementarity; Interior-point; Path-following; Full-Newton step; 90C33; 90C51 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10957-020-01728-4

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