期刊名称：CORE Discussion Papers / Center for Operations Research and Econometrics (UCL), Louvain
出版年度：2009
卷号：1
出版社：Center for Operations Research and Econometrics (UCL), Louvain
摘要：In this paper, we establish a local quadratic convergence of polynomial-time interior-point
methods for general conic optimization problems. The main structural property used in our
analysis is the logarithmic homogeneity of self-concordant barrier functions. We propose new
path-following predictor-corrector schemes which work only in the dual space. They are based on
an easily computable gradient proximity measure, which ensures an automatic transformation of
the global linear rate of convergence to the local quadratic one under some mild assumptions. Our
step-size procedure for the predictor step is related to the maximum step size (the one that takes
us to the boundary). It appears that in order to obtain local superlinear convergence, we need to
tighten the neighborhood of the central path proportionally to the current duality gap.
