New complexity analysis of a full-Newton step feasible interior-point algorithm for P∗(κ)-LCP

• Published in: Optimization letters Vol. 9; no. 6; pp. 1105 - 1119
• Main Authors: Wang, G. Q., Fan, X. J., Zhu, D. T., Wang, D. Z.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2015
• Subjects: Computational Intelligence; Mathematics; Mathematics and Statistics; Numerical and Computational Physics; Operations Research/Decision Theory; Optimization; Original Paper; Simulation; Polynomial complexity; Interior-point methods; Linear complementarity problem; matrix; Full-Newton step
• ISSN: 1862-4472; 1862-4480
• DOI: 10.1007/s11590-014-0800-4

In this paper, we consider a full-Newton step feasible interior-point algorithm for P ∗ ( κ ) -linear complementarity problem. The perturbed complementarity equation x s = μ e is transformed by using a strictly increasing function, i.e., replacing x s = μ e by ψ ( x s ) = ψ ( μ e ) with ψ ( t ) = t , and the proposed interior-point algorithm is based on that algebraic equivalent transformation. Furthermore, we establish the currently best known iteration bound for P ∗ ( κ ) -linear complementarity problem, namely, O ( ( 1 + 4 κ ) n log n ε ) , which almost coincides with the bound derived for linear optimization, except that the iteration bound in the P ∗ ( κ ) -linear complementarity problem case is multiplied with the factor ( 1 + 4 κ ) .