Majorization-Minimization Procedures and Multi-Objective Optimization

Abstract

This project revolved around so-called majorization-minimization methods in optimization. These types of methods are of particular importance in machine learning and statistics and applicable to a wide range of Air Force applications. In particular, Jerome established rigorous convergence results and convergence rates for a variety of non-convex problems encountered in image and phase retrieval problems. Such theoretical results guide and underpin the engineering application of these algorithms. In all, this project produced 12 journal articles, many in top journals (2 in Mathematical Programming and 2 in SIAM Optimization). Most notably, during the second year of the project, Jrme Bolte was awarded the SIAM Optimization prize with S. Sabach and M. Teboulle, for the paper Proximal Alternating Linearized Minimization for Nonconvex and Nonsmooth Problems.' Jerome will be continuing similar work with a follow-on AFOSR grant. A full list of papers and results can be found in the attached report.

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Document Details

Document Type
Technical Report
Publication Date
Mar 05, 2019
Accession Number
AD1087598

Entities

People

  • Jerome Bolte

Tags

Communities of Interest

  • Autonomy

DTIC Thesaurus Topics

  • Air Force
  • Air Force Research Laboratories
  • Algorithms
  • Computer Programming
  • Convergence
  • Evolutionary Algorithms
  • Inequalities
  • Information Processing
  • Machine Learning
  • Mathematical Programming
  • Mathematics
  • Multiobjective Optimization
  • Nonlinear Programming
  • Operations Research
  • Optimization
  • Signal Processing
  • Systems Engineering

Readers

  • Academic Conference Management
  • Distributed Systems and Data Platform Development
  • Graph Algorithms and Convex Optimization.

Technology Areas

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