Extending Accelerated Optimization into the PDE Framework

Abstract

The primary goal is to extend momentum based methods (Heavy Ball, and Nesterov) from the finite dimensional framework into the infinite dimensional framework of gradient based optimization over the manifolds of functions, curves, surfaces, diffeomorphisms, and other distributed unknowns. This includes developing 1) a theory of PDE methods for accelerated gradient optimization 2) formulation of the specific PDE equations for the application of this theory in several optimization contexts 3) numerical methods for solving accelerated PDE systems 4) theoretical analysis of convergence rates and performance gains 5) development of efficient implementations amenable to parallel computing.

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Document Details

Document Type
Technical Report
Publication Date
Sep 23, 2021
Accession Number
AD1197255

Entities

People

  • Anthony Yezzi

Organizations

  • Georgia Tech Research Corporation

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  • Calculus
  • Calculus Of Variations
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Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)