An Explicit Convergence Rate for Nesterov's Method from SDP
2018 IEEE International Symposium on Information Theory (ISIT)(2018)
摘要
The framework of Integral Quadratic Constraints (IQC) introduced by Lessard et al. (2014) reduces the computation of upper bounds on the convergence rate of several optimization algorithms to semi-definite programming (SDP). In particular, this technique was applied to Nesterov's accelerated method (NAM). For quadratic functions, this SDP was explicitly solved leading to a new bound on the convergence rate of NAM, and for arbitrary strongly convex functions it was shown numerically that IQC can improve bounds from Nesterov (2004). Unfortunately, an explicit analytic solution to the SDP was not provided. In this paper, we provide such an analytical solution, obtaining a new general and explicit upper bound on the convergence rate of NAM, which we further optimize over its parameters. To the best of our knowledge, this is the best, and explicit, upper bound on the convergence rate of NAM for strongly convex functions.
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关键词
NAM,explicit convergence rate,Nesterov's method,SDP,Integral Quadratic Constraints,IQC,semidefinite programming,Nesterov's accelerated method,quadratic functions,arbitrary strongly convex functions,explicit analytic solution
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