complexity analysis of primal-dual interior-point methods for convex quadratic programming based on a new twice parameterized kernel function

In this paper, we present primal-dual interior-point methods (ipms) for convex quadratic programming (cqp) based on a new twice parameterized kernel function (kf) with a hyperbolic barrier term.  to our knowledge, this is the first kf with a twice parameterized hyperbolic barrier term. by using some conditions and simple analysis, we derive the currently best-known iteration bounds for large- and small-update methods, namely, textbf{o}big(sqrt{n}log nlogfrac{n}{epsilon}big) and textbf{o}big(sqrt{n}logfrac{n}{epsilon}big), respectively, with  special choices of the parameters. finally, some numerical results regarding the practical performance of the new proposed kf are reported.