A New full-newton step infeasible interior-point method for P∗(κ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_*(\\kappa )$$\\end{document}-linear Complementarity problem

Abstract

In this paper, we suggest a new infeasible interior-point method (IIPM) for P∗(κ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_{*}(\\kappa )$$\\end{document}-linear complementarity problem (P∗(κ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_{*}(\\kappa )$$\\end{document}-LCP) based on a new class of kernel functions with full-Newton steps. Each iteration of the algorithm consists of a feasible step and a few centering steps. The feasible step is defined by the newly proposed kernel functions, while the centering step is determined by using Newton’s method. New class of kernel functions includes a logarithmic kernel function in Roos (SIAM J Optim 16:1110–1136, 2006) and a trigonometric kernel function in Moslemi and Kheirfam (Optim Lett 13:127–157, 2019), Kheirfam and Haghighi (Commun Comb Optim 3:51–70, 2018), Fathi-Hafshejani et al. (J Appl Math Comput 48:111–128, 2015) as special cases. And we show that the proposed algorithm has the best known complexity for P∗(κ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_*(\\kappa )$$\\end{document}-LCP for such a method and present some numerical results.