Structured Assignment: Geometric Optimization Algorithms for Large-Scale Matching

Abstract

This project aimed to develop a mathematical theory and accompanying numerical algorithms for geometrically structured instances of the assignment problem. We considered generalizations of assignment/transportation mathematical programs that included a variety of objective functions, with the commonality that they are parameterized by an underlying distance function along a geometric domain. This additional assumption--which arises naturally in applications including 3D shape analysis, logistical operations/planning, and machine learning--provides added structure that we leveraged to derive fine-grained understanding of the energy landscape and tractability.

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Document Details

Document Type
Technical Report
Publication Date
Dec 20, 2023
Accession Number
AD1230554

Entities

People

  • Justin Solomon

Organizations

  • Massachusetts Institute of Technology

Tags

Readers

  • Computer Vision.
  • Neural Network Machine Learning.
  • Theoretical Analysis.

Technology Areas

  • AI & ML
  • AI & ML - Machine Learning Algorithms