Infeasible path-following interior point algorithm for Cartesian P_*(κ) nonlinear complementarity problems over symmetric cones

ABSTRACT

In this paper, we establish a theoretical framework of infeasible path-following interior point algorithm for Cartesian $P_{\ast }\left(\kappa \right)$ nonlinear complementarity problems over symmetric cones using a wide neighbourhood of the central path. In order to prove the convergence of the proposed algorithm, we propose a scaled Lipschitz condition which has scaling invariance. Under the condition, we estimate the iteration complexities of the proposed algorithm and provide some numerical results. The numerical results show that the algorithm is efficient and reliable.

KEYWORDS:

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

2010 AMS SUBJECT CLASSIFICATIONS:

• 90C33
• 90C51

Disclosure statement

No potential conflict of interest was reported by the authors.