On the Superlinear Convergence of Interior Point Algorithms for a General Class of Problems
In this paper, we extend the Q-superlinear convergence theory recently developed by Zhang, Tapia and Dennis for a class of interior point linear programming algorithms to similar interior point algorithms for quadratic programming and for linear complementarity problems. Our unified approach consists of viewing all these algorithms as the damped Newton method applied to perturbations of a general problem. We show that under appropriate assumptions, Q-superlinear convergence can be achieved by asymptotically taking the step to the boundary of the positive orthant and letting the barrier (or path-following) parameter approach zero at a specific rate.
Citable link to this pagehttps://hdl.handle.net/1911/101674
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