An interior point method for $$P_{*}(\kappa )$$-horizontal linear complementarity problem based on a new proximity function

Autor:	Alireza Fakharzadeh Jahromi, Sajad Fathi Hafshejani
Rok vydání:	2019
Předmět:	Combinatorics Computational Mathematics Simple (abstract algebra) Applied Mathematics Path (graph theory) Convex optimization Trigonometric functions Function (mathematics) Binary logarithm Linear complementarity problem Interior point method Mathematics
Zdroj:	Journal of Applied Mathematics and Computing. 62:281-300
ISSN:	1865-2085 1598-5865
DOI:	10.1007/s12190-019-01284-9
Popis:	Kernel functions play an important role in the design and complexity analysis of interior point algorithms for solving convex optimization problems. They determine both search directions and the proximity measure between the iterate and the central path. In this paper, we introduce a primal-dual interior point algorithm for solving $$P_*(\kappa ) $$-horizontal linear complementarity problems based on a new kernel function that has a trigonometric function in its barrier term. By using some simple analysis tools, we present some properties of the new kernel function. Our analysis shows that the algorithm meets the best known complexity bound i.e., $$O\left( (1+2\kappa )\sqrt{n}\log n\log \frac{n}{\varepsilon }\right) $$ for large-update methods. Finally, we present some numerical results illustrating the performance of the algorithm.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::56879967df6af3a617aee0cc6cf784c9 https://doi.org/10.1007/s12190-019-01284-9 Zobrazit plný text záznamu Full text from SpringerLink