Geometric Optimization and Combinatorial Homological Programming

Abstract

New mathematical methods for distributed optimization and related problems were generated using concepts from algebraic topology and sheaf theory. In particular, the Hodge Laplacian was extended to sheaves of data in the context of distributed optimization, indoor mapping, network communications, and learning. The results greatly extend known results from spectral graph theory and simultaneous localization and mapping.

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Document Details

Document Type
Technical Report
Publication Date
Oct 03, 2019
Accession Number
AD1090239

Entities

People

  • Robert Ghrist

Organizations

  • University of Pennsylvania

Tags

Communities of Interest

  • Autonomy
  • Materials and Manufacturing Processes
  • Space

DTIC Thesaurus Topics

  • Air Force
  • Air Force Research Laboratories
  • Algebraic Topology
  • Applied Mathematics
  • Artificial Intelligence
  • Cartography
  • Communication Networks
  • Computer Programming
  • Geometry
  • Governments
  • Graph Theory
  • Information Systems
  • Learning
  • Optimization
  • Topology
  • Vector Spaces
  • Wireless Networks

Readers

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