Primal-dual entropy-based interior-point algorithms for linear optimization

We propose a family of search directions based on primal-dual entropy in the contextof interior-point methods for linear optimization. We show that by using entropy based searchdirections in the predictor step of a predictor-corrector algorithm together with a homogeneousself-dual embedding, we can achieve the current best iteration complexity bound for linear opti-mization. Then, we focus on some wide neighborhood algorithms and show that in our family ofentropy based search directions, we can find the best search direction and step size combinationby performing a plane search at each iteration. For this purpose, we propose a heuristic planesearch algorithm as well as an exact one. Finally, we perform computational experiments tostudy the performance of entropy-based search directions in wide neighborhoods of the centralpath, with and without utilizing the plane search algorithms.