Mixed-Integer Polynomial Optimization- Structure and Algorithms
Abstract
Over the past 60 years, the ability to efficiently solve discrete optimization problems has increased dramatically. In particular, the field of mixed-integer linear programming (MILP) has experienced great success from theoretical, computational, and applied viewpoints. This same success has not been realized for the more general case of mixed-integer polynomial programming (MIPP), which allows for polynomial objective functions. In fact, very few classes of MIPP can be solved effectively. This inability to solve MIPP is unfortunate since polynomial objectives can be used to model and-or approximate various nonlinear cost functions. In fact, MIPP problems arise in such areas as operations research, engineering, computer science, physics, biology, finance, and economics. Various DoD and Air Force applications include those arising in mission planning, command and control, logistics, and resource allocation. The effort seeks to bridge the gap between MILP and MIPP on both theoretical and algorithmic levels. Specifically, the plan is to first obtain fundamental structural results to lay the mathematical foundation, and to then leverage these results to design efficient exact and approximation algorithms for important classes of MIPP problems. Of particular interest are the Boolean matrix and tensor factorization problems, which are of general interest in mathematical optimization and data science.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Mar 06, 2024
- Source ID
- FA95502310433
Entities
People
- Alberto Del Pia
Organizations
- Air Force Office of Scientific Research
- United States Air Force
- University of Wisconsin System