Solution of Heaviside Composite Optimization Problems, Complementarity Constraints, and Conditional Stochastic Programs, with Improvement by Progressive Integer Programming
Abstract
As a next step beyond the PI s study of modern nonconvex and nondifferentiable optimization under previous AFOSR support, this project proposes and investigates a novel progressive integer programming (PIP) based method for solving several advanced classes of mathematical optimization problems that are broadly applicable to the modeling of a host of practical applications. These include the design of classification and treatment rules with domain constraints, the quantization of physical phenomena, scenario changes in uncertain environments, and the expression of probability functions as expectations for optimal decision making under uncertainty. The problems being studied all fall outside the normal scope of optimization problems with favorable functional properties - most prominently, convexity and differentiability; their successful treatment requires the fusion of methods from the continuous, discrete, and stochastic optimization domains. Preliminary results provide compelling evidence for the promise of the proposed method in speed and ability for solving problems of large sizes.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 06, 2025
- Source ID
- FA95502510022
Entities
People
- Jong-shi Pang
Organizations
- Air Force Office of Scientific Research
- United States Air Force
- University of Southern California