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A predictor-corrector path following algorithm for symmetric optimization based on darvay's technique

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In this paper, we present a predictor-corrector path-following interior-point algorithm for symmetric cone optimization based on Darvay's technique. Each iteration of the algorithm contains a predictor step and a corrector step based on a modification of the Nesterov and Todd directions. | Yugoslav Journal of Operations Research 24 (2014) Number 1, 35-51 DOI: 10.2298/YJOR120904016K A PREDICTOR-CORRECTOR PATH-FOLLOWING ALGORITHM FOR SYMMETRIC OPTIMIZATION BASED ON DARVAY'S TECHNIQUE BEHROUZ KHEIRFAM Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. Iran, b.kheirfam@azaruniv.edu Received: September 2012 / Accepted: March 2013 Abstract: In this paper, we present a predictor-corrector path-following interior-point algorithm for symmetric cone optimization based on Darvay's technique. Each iteration of the algorithm contains a predictor step and a corrector step based on a modification of the Nesterov and Todd directions. Moreover, we show that the algorithm is well defined and that the obtained iteration bound is Jordan algebra. √ log , where Keywords: Symmetric cone optimization, interior-point method, polynomial complexity. is the rank of Euclidean predictor-corrector method, MSC: 90C51. 1. INTRODUCTION In recent years, there have been extensive investigations concerning the analysis of interior-point methods (IPMs) for symmetric cone optimization (SCO). A few optimization problems are special cases of symmetric cones, such as nonnegative orthants, linear optimization (LO), semidefinite optimization (SDO) and second-order cone optimization (SOCO). Basic idea for solving SCO is using feasible interior-point method, as used by Nesterov and Nemirovskii [9]. Their method was primarily either primal or dual based. Later on, Nesterov and Todd [10] proposed symmetric interiorpoint algorithms on a special class of convex optimization problems, where the associated cone is self-scaled. Later on, it was observed that these cones were precisely 36 B. Kheirfam / A Predictor-corrector path-following algorithm symmetric cones [3]. Thus, Nesterov and Todd algorithm was the first primal-dual interior-point algorithm for optimization over symmetric cones. Monteiro and Zhang [8] designed a interior-point path-following algorithm for