Convergence and polynomiality of primal-dual interior-point algorithms for linear programming with selective addition of inequalities

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...

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...

A Primal-Dual Interior Point Algorithm for Linear Programming

This chapter presents an algorithm that works simultaneously on primal and dual linear programming problems and generates a sequence of pairs of their interior feasible solutions. Along the sequence generated, the duality gap converges to zero at least linearly with a global convergence ratio (1 Yf/n); each iteration reduces the duality gap by at least Yf/n. Here n denotes the size of the probl...

Primal-dual entropy-based interior-point algorithms for linear optimization

We propose a family of search directions based on primal-dual entropy in the contextof interior-point methods for linear optimization. We show that by using entropy based searchdirections in the predictor step of a predictor-corrector algorithm together with a homogeneousself-dual embedding, we can achieve the current best iteration complexity bound for linear opti-mization. The...

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