It is well known that a large neighborhood interior point algorithm for linear optimization performs much better in implementation than its small neighborhood counterparts. One of the key elements of interior point algorithms is how to update the barrier parameter. The main goal of this paper is to introduce an “adaptive” long step interior-point algorithm in a large neighborhood of central pat...

This article studies the linear multicommodity network flow problem. This kind of problem arises in a wide variety of contexts. A numerical implementation of the primal-dual interior-point method is designed to solve the problem. In the interior-point method, at each iteration, the corresponding linear problem, expressed as an augmented indefinite system, is solved by using the AINV algorithm c...

We perform a smoothed analysis of the termination phase of an interior-point method. By combining this analysis with the smoothed analysis of Renegar’s interior-point algorithm in [DST02], we show that the smoothed complexity of an interior-point algorithm for linear programming is O(m log(m/σ)). In contrast, the best known bound on the worst-case complexity of linear programming is O(mL), wher...

In this paper, we propose a second-order corrector interior-point algorithm for semidefinite programming (SDP). This algorithm is based on the wide neighborhood. The complexity bound is O( √ nL) for the Nesterov-Todd direction, which coincides with the best known complexity results for SDP. To our best knowledge, this is the first wide neighborhood second-order corrector algorithm with the same...

In this paper, a new weighted short-step primal-dual interior point algorithm for convex quadratic optimization (CQO) problems is presented. The algorithm uses at each interior point iteration only full-Newton steps and the strategy of the central path to obtain an ε-approximate solution of CQO. This algorithm yields the best currently wellknown theoretical iteration bound, namely, O( √ n log ε...

In this paper, we consider convex quadratic semidefinite optimization problems and provide a primal-dual Interior Point Method (IPM) based on a new kernel function with a trigonometric barrier term. Iteration complexity of the algorithm is analyzed using some easy to check and mild conditions. Although our proposed kernel function is neither a Self-Regular (SR) fun...

In this paper we use interior-point methods for linear programming, developed in t,he contest of sequential computation, to obtain a parallel algorithm for t,he bipartite matching problem. Our algorithm runs in 0*(,/E) time I. Our results extend to the weighted bipartite matching problem and to the zero-one minimum-cost flow problem, yielding O*( filog C’) algorithms?. This improvk’previous bou...

This paper studies a new potential-function and an infeasible-interior-point method based on this function for the solution of linear programming problems. This work is motivated by the apparent gap between the algorithms with the best worst-case complexity and their most successful implementations. For example, analyses of the algorithms are usually carried out by imposing several regularity a...

We propose a new infeasible path-following algorithm for convex linearlyconstrained quadratic programming problem. This algorithm utilizes the monomial method rather than Newton's method for solving the KKT equations at each iteration. As a result, the sequence of iterates generated by this new algorithm is infeasible in the primal and dual linear constraints, but, unlike the sequence of iterat...

In this paper, we propose a feasible primal-dual path-following algorithm for convex quadratic programs.At each interior-point iteration the algorithm uses a full-Newton step and a suitable proximity measure for tracing approximately the central path.We show that the short-step algorithm has the best known iteration bound,namely O( √ n log (n+1) ).