학술논문
A class of new search directions for full-NT step feasible interior point method in semidefinite optimization.
Document Type
Journal
Author
Guerra, Loubna (DZ-BBAMI-RO) AMS Author Profile
Source
Subject
65 Numerical analysis -- 65K Mathematical programming, optimization and variational techniques
65K10Optimization and variational techniques
90Operations research, mathematical programming -- 90C Mathematical programming
90C22Semidefinite programming
90C25Convex programming
65K10
90
90C22
90C25
Language
English
Abstract
Summary: ``In this paper, based on Darvay {\it et al.}'s strategy for linear optimization (LO) (Z. Darvay and P. R. Takács, {\it Optim. Lett.} {\bf 12} (2018) 1099--1116.) [MR3819678], we extend Kheirfam {\it et al.}'s feasible primal-dual path-following interior point algorithm for LO (B. Kheirfam and A. Nasrollahi, {\it Asian-Eur. J. Math.} {\bf 1} (2020) 2050014.) [MR4057676] to semidefinite optimization (SDO) problems in order to define a class of new search directions. The algorithm uses only full Nesterov-Todd (NT) step at each iteration to find an $\epsilon$-approximated solution to SDO. Polynomial complexity of the proposed algorithm is established which is as good as the LO analogue. Finally, we present some numerical results to prove the efficiency of the proposed algorithm.''