On the Superlinear and Quadratic Convergence of Primal-Dual Interior Point Linear Programming Algorithms

Superlinear Convergence of Primal-Dual Interior Point Algorithms for Nonlinear Programming

Local and superlinear convergence of a primal-dual interior point method for nonlinear semidefinite programming

In this paper, we consider a primal-dual interior point method for solving nonlinear semidefinite programming problems. We propose primal-dual interior point methods based on the unscaled and scaled Newton methods, which correspond to the AHO, HRVW/KSH/M and NT search directions in linear SDP problems. We analyze local behavior of our proposed methods and show their local and superlinear conver...

Theoretical convergence of large-step primal-dual interior point algorithms for linear programming

This paper proposes two sets of rules Rule G and Rule P for controlling step lengths in a generic primal dual interior point method for solving the linear program ming problem in standard form and its dual Theoretically Rule G ensures the global convergence while Rule P which is a special case of Rule G ensures the O nL iteration polynomial time computational complexity Both rules depend only o...

On the Convergence of an Inexact Primal-Dual Interior Point Method for Linear Programming

The inexact primal-dual interior point method which is discussed in this paper chooses a new iterate along an approximation to the Newton direction. The method is the Kojima, Megiddo, and Mizuno globally convergent infeasible interior point algorithm The inexact variation is shown to have the same convergence properties accepting a residual in both the primal and dual Newton step equation also ...

ABS Solution of equations of second kind and application to the primal-dual interior point method for linear programming

 Abstract  We consider an application of the ABS procedure to the linear systems arising from the primal-dual interior point methods where Newton method is used to compute path to the solution. When approaching the solution the linear system, which has the form of normal equations of the second kind, becomes more and more ill conditioned. We show how the use of the Huang algorithm in the ABS cl...