Work

An Explicit Convergence Rate for Nesterov's Method from SDP

Year: 2018

Type: conference-paper

Abstract: 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.

Source: IEEE International Symposium on Information Theory (ISIT)

DOI: 10.1109/isit.2018.8437794

Authors: Sam Safavi, Bikash Joshi, Guilherme França, José Bento

Institution: Princeton University

Language: English

Topic: Advanced Optimization Algorithms Research

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, National Institutes of Health, National Institute of Allergy and Infectious Diseases

Awards: Predicting the emergence of antibiotic resistance through multi-omics approaches and Immune System-surveillan, BIGDATA: F: Collaborative Research: Design and Computation of Scalable Graph Distances in Metric Spaces: A Unified Multiscale Interpretable Perspective