Interior-Point Methods(IPMs)not only are the most effective methods in practice but also have polynomial-time complexity.Many researchers have proposed IPMs for Linear Optimization(LO)and achieved plentiful results.In...Interior-Point Methods(IPMs)not only are the most effective methods in practice but also have polynomial-time complexity.Many researchers have proposed IPMs for Linear Optimization(LO)and achieved plentiful results.In many cases these methods were extendable for LO to Linear Complementarity Problems(LCPs)successfully.In this paper,motivated by the complexity results for linear optimization based on the study of H.Mansouri et al.(Mansouri and Zangiabadi in J.Optim.62(2):285–297,2013),we extend their idea for LO to LCP.The proposed algorithm requires two types of full-Newton steps are called,feasibility steps and(ordinary)centering steps,respectively.At each iteration both feasibility and optimality are reduced exactly at the same rate.In each iteration of the algorithm we use the largest possible barrier parameter valueθwhich lies between the two values 117n and 113n,this makes the algorithm faster convergent for problems having a strictly complementarity solution.展开更多
基金The authors are indebted to the referees for their careful reading of the manuscript and for their suggestions which helped to improve the paper.The authors also wish to thank Shahrekord University for financial support.
文摘Interior-Point Methods(IPMs)not only are the most effective methods in practice but also have polynomial-time complexity.Many researchers have proposed IPMs for Linear Optimization(LO)and achieved plentiful results.In many cases these methods were extendable for LO to Linear Complementarity Problems(LCPs)successfully.In this paper,motivated by the complexity results for linear optimization based on the study of H.Mansouri et al.(Mansouri and Zangiabadi in J.Optim.62(2):285–297,2013),we extend their idea for LO to LCP.The proposed algorithm requires two types of full-Newton steps are called,feasibility steps and(ordinary)centering steps,respectively.At each iteration both feasibility and optimality are reduced exactly at the same rate.In each iteration of the algorithm we use the largest possible barrier parameter valueθwhich lies between the two values 117n and 113n,this makes the algorithm faster convergent for problems having a strictly complementarity solution.
