The Notion of the Quasicentral Path in Linear Programming

EasyChair Preprint 9120

Abstract

The notion of the central path plays an important role in the development of most primaldual

interior point algorithms. In this work we prove that a related notion called the quasicentral

path, introduced by Argaez and Tapia in nonlinear programming, while being a less restrictive

notion is suciently strong to guide the iterates towards a solution of the linear program. We

use a new merit function for advancing to the quasicentral path, and weighted neighborhoods

as proximity measures of this central region. We prove global convergence theory, and present

numerical results that demonstrate the eectiveness of the algorithm.

Keyphrases: Interior point methods, Newton's method, Primal-Dual Methods, linear programming

@booklet{EasyChair:9120,
  author    = {Miguel Argaez and Oswaldo Mendez and Leticia Velazquez},
  title     = {The Notion of the Quasicentral Path in Linear Programming},
  howpublished = {EasyChair Preprint 9120},
  year      = {EasyChair, 2022}}