Convex Minimization With Good Complexity: Self-concordant Barriers
The efficiency of iterative methods is poor for the class of convex problems, because this class includes "bad guys" whose minimum cannot be approximated without a large number of function and subgradient evaluations; thus, to have practically appealing efficiency results, it is necessary to make additional restrictions on the class of problems. Two such classes are problems special barrier functions, first self-concordant barrier functions, according to the theory of Nesterov and Nemirovskii, and second self-regular barrier functions according to the theory of Terlaky and coauthors.
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