Algorithms and Complexity in Mixed-Integer Polynomial Optimization

Abstract

Mixed-integer nonlinear optimization encompasses a large family of mathematical programming problems that arise in such scenarios as artificial intelligence, inventory routing, production planning, resource allocation, and supply chain management. These problems are extremely challenging to solve due to both the discrete nature of the decision variables and the nonlinearities in the objective function and constraints. This effort will investigate the complexity of solving various such classes of problems and will develop new theory and algorithms for obtaining more efficient techniques. The research will focus on three main directions: (1) complexity and theoretical results for nonlinear integer programs, (2) generalized theory for polynomial integer settings, and (3) improved cutting planes from extended formulations. Emphasis will be directed towards overcoming the challenging hurdle of nonconvexity.

Document Details

Document Type
DoD Grant Award
Publication Date
Jan 21, 2022
Source ID
FA95502110107XX0

Entities

People

  • Robert Hildebrand

Organizations

  • Air Force Office of Scientific Research
  • United States Air Force
  • Virginia Tech

Tags

Readers

  • Operations Research
  • Systems Analysis and Design

Technology Areas

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