# A primal-dual large-update interior-point algorithm for P *(κ)-LCP based on a new class of kernel functions

A primal-dual large-update interior-point algorithm for P *(κ)-LCP based on a new class of kernel... In this paper, we propose a large-update primal-dual interior point algorithm for P *(κ)-linear complementarity problem. The method is based on a new class of kernel functions which is neither classical logarithmic function nor self-regular functions. It is determines both search directions and the proximity measure between the iterate and the center path. We show that if a strictly feasible starting point is available, then the new algorithm has $$o\left( {(1 + 2k)p\sqrt n {{\left( {\frac{1}{p}\log n + 1} \right)}^2}\log \frac{n}{\varepsilon }} \right)$$ o ( ( 1 + 2 k ) p n ( 1 p log n + 1 ) 2 log n ε ) iteration complexity which becomes $$o\left( {(1 + 2k)\sqrt n log{\kern 1pt} {\kern 1pt} n\log \frac{n}{\varepsilon }} \right)$$ o ( ( 1 + 2 k ) n l o g n log n ε ) with special choice of the parameter p. It is matches the currently best known iteration bound for P *(κ)-linear complementarity problem. Some computational results have been provided. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

# A primal-dual large-update interior-point algorithm for P *(κ)-LCP based on a new class of kernel functions

, Volume 34 (1) – Mar 8, 2018
16 pages

/lp/springer-journals/a-primal-dual-large-update-interior-point-algorithm-for-p-lcp-based-on-btQXtduf9g
Publisher
Springer Journals
Copyright © 2018 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-018-0729-y
Publisher site
See Article on Publisher Site

### Abstract

In this paper, we propose a large-update primal-dual interior point algorithm for P *(κ)-linear complementarity problem. The method is based on a new class of kernel functions which is neither classical logarithmic function nor self-regular functions. It is determines both search directions and the proximity measure between the iterate and the center path. We show that if a strictly feasible starting point is available, then the new algorithm has $$o\left( {(1 + 2k)p\sqrt n {{\left( {\frac{1}{p}\log n + 1} \right)}^2}\log \frac{n}{\varepsilon }} \right)$$ o ( ( 1 + 2 k ) p n ( 1 p log n + 1 ) 2 log n ε ) iteration complexity which becomes $$o\left( {(1 + 2k)\sqrt n log{\kern 1pt} {\kern 1pt} n\log \frac{n}{\varepsilon }} \right)$$ o ( ( 1 + 2 k ) n l o g n log n ε ) with special choice of the parameter p. It is matches the currently best known iteration bound for P *(κ)-linear complementarity problem. Some computational results have been provided.

### Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Mar 8, 2018

### References

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