Splitting Enables Overcoming the Curse of Dimensionality

Abstract

In this short note we briey outline a new and remarkably fast algorithm for solving a a large class of high dimensional Hamilton-Jacobi (H-J) initial value problems arising in optimal control and elsewhere [1]. This is done without the use of grids or numerial approximations. Moreover, by using the level set method [8] we can rapidly compute projections of a point in Rn, n large to a fairly arbitrary compact set [2]. The method seems to generalize widely beyond what will we present here to some nonconvex Hamiltonians, state dependent Hamiltonians, differential games and perhaps new linear programming algorithms.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 2015
Accession Number
AD1003389

Entities

People

  • Jérôme Darbon
  • Stanley Osher

Organizations

  • University of California

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Computer Programming
  • Convex Sets
  • Equations
  • Evolutionary Algorithms
  • Geometry
  • Heuristic Methods
  • Identities
  • Linear Programming
  • Mathematical Analysis
  • Mathematics
  • Optimization
  • Sequences
  • Splitting
  • Test And Evaluation
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

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