The Notion of the Quasicentral Path in Linear Programming

The notion of the central path plays an important role in the development of most primal-dual 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 it is sufficiently strong to guide the iterates towards a solution of the problem. 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 some numerical results that demonstrate the effectiveness of the algorithm.