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Tianxiao Sun Globally convergent Newton-type methods for convex optimization based on smoothness structures We study the smooth structure of convex functions by generalizing a powerful concept so-called self-concordance introduced by Nesterov and Nemirovskii to a broader class of convex functions. The proposed theory provides a mathematical tool to analyze both local and global convergence of Newton-type methods as long as the underlying functionals fall into our generalized self-concordant function class. First, we introduce the class of generalized self-concordant functions, which…Find out more »