Infeasible Mehrotra-type predictor–corrector algorithm for cartesian P_*(κ) nonlinear complementarity problems over symmetric cones

ABSTRACT

This paper establishes a theoretical framework of infeasible Mehrotra-type predictor–corrector algorithm for Cartesian $P_{\ast }\left(\kappa \right)$ nonlinear complementarity problems over symmetric cones which can be regarded as an extension of Liu et al. [Polynomial convergence of Mehrotra-type predictor–corrector algorithm for the Cartesian $P_{\ast }\left(\kappa \right)$-LCP over symmetric cones, Optimization 64(4) (2013), pp. 1–23] for Cartesian $P_{\ast }\left(\kappa \right)$ linear complementarity problems over symmetric cones to Cartesian $P_{\ast }\left(\kappa \right)$ nonlinear complementarity problems over symmetric cones. The iteration complexities of the proposed algorithm are estimated and some numerical results are provided. The numerical results show that the proposed algorithm is efficient and reliable.

KEYWORDS:

• Cartesian $P_{\ast }\left(\kappa \right)$
• nonlinear complementarity problem
• predictor–corrector
• interior point algorithm
• symmetric cone

2010 AMS SUBJECT CLASSIFICATIONS:

• 90C33
• 90C51

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work supported by the Natural Science Foundation of Shaanxi Province [Grant 2017JM1014].