An O nL iteration primal- dual path- following method, based on wide neighbourhood and large update, for second- order cone programming

In this article we propose a new primal-dual path-following interior point algorithm for second-order cone programming. Each iterate always follows the usual wide neighborhood Nu(-)(infinity)(tau), it does not necessarily stay within it, but must stay within the wider neighbourhood Nu(tau, beta). We show that the algorithm has Omicron(root nL) iteration complexity bound which is better than that of usual wide neighbourhood algorithm O(n log epsilon(-1)), where n is the dimension of the problem, L = 1/alpha log x(0)(T) s0/epsilon with epsilon the required precision, alpha is an element of[0, 1] the given constant number and (x(0), s(0)) the initial interior solution. It is the best result in regard to the iteration complexity bound in the context of path-following method for second-order cone programming.