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Polynomial Convergence of Primal-Dual Algorithms for Semidefinite Programming Based on the Monteiro and Zhang Family of Directions
SIAM Journal on Optimization
This paper establishes the polynomialconvergence of the class of primal-dualfeasible interiorpoint algorithms for semide nite programming (SDP) based on Monteiro and Zhang family of search directions. In contrast to Monteiro and Zhang's work, no condition is imposed on the scaling matrix that determines the search direction. We show that the polynomial iterationcomplexity bounds of two well-known algorithms for linear programming, namely the short-step path-following algorithm of Kojima et al.doi:10.1137/s1052623496308618 fatcat:i3yki5rovncx7ebllu3xfgahiy