An arc-search infeasible interior-point algorithm for horizontal linear complementarity problem in the N∞− neighbourhood of the central path

ABSTRACT

An arc-search infeasible interior point algorithm is proposed for solving a horizontal linear complementarity problem. The algorithm produces a sequence of iterates in the negative infinity neighbourhood of the central path and searches the solutions along the ellipses that approximate the whole central path. We study the theoretical convergence properties and also establish polynomial complexity bound for the proposed algorithm. Moreover, our numerical results suggest that the proposed algorithm is very efficient and competitive.

KEYWORDS:

• Horizontal linear complementarity problem
• Arc-search direction
• wide neighbourhood
• infeasible interior-point methods
• polynomial complexity

2010 AMS SUBJECT CLASSIFICATIONS:

• 90C51
• 90C33

Disclosure statement

No potential conflict of interest was reported by the author.