The framework of Integral Quadratic Constraints (IQC) introduced by (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.
Finally, @cite_7 gives a possible geometric interpretation of why NAM accelerates convergence. For their NAM-type method, the result @math is obtained, basically re-deriving .
@cite_7
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Protocol design requires understanding state distributed across many nodes, complex message exchanges, and with competing traAEc. Traditional analysis tools (such as packet traces) too often hide protocol dynamics in a mass of extraneous detail. This paper presents nam , a network animator that provides packet-level animation and protocol-speci c graphs to aid the design and debugging of new network protocols. Taking data from network simulators (such as ns) or live networks, nam was one of the rst tools to provide general purpose, packet-level, network animation. Nam now integrates traditional time-event plots of protocol actions and scenario editing capabilities. We describe how nam visualizes protocol and network dynamics.