A Full-Newton Step Interior-point Method Based on a Class of Specific Algebra Transformation

Article type: Research Article

Authors: Kheirfam, Behrouz^{; *} | Nasrollahi, Afsaneh

Affiliations: Department of Applied Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. Iran. [email protected]

Correspondence: [*] Address for correspondence: Department of Applied Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. Iran.

Abstract: We present a primal-dual path-following interior-point method for linear optimization that is based on the integer powers of the square root function. Our derived search directions is a generalization of the standard directions and the search directions given by Darvay. The proposed algorithm uses only full steps and hence no need to perform line search. We first prove that the iterates lie in the quadratic convergence neighborhood of the proximity measure and then derive the iteration-complexity bound for the algorithm.

Keywords: Linear optimization, full-Newton step, feasible interior-point method, small-update methods, polynomial complexity

DOI: 10.3233/FI-2018-1747

Journal: Fundamenta Informaticae, vol. 163, no. 4, pp. 325-337, 2018