Optimization Problems with Complex Functional Constraints- Addressing Hierarchy and Risk
Abstract
Optimization has assumed profound relevance in DoD settings in the context of design, planning, and operational settings. Instances of such problems include (i) logistics management in networked regimes complicated by delays and uncertainty; and (ii) resource allocation in risk-afflicted environments, complicated by the presence of malicious adversaries. Such problems necessitate minimizing or maximizing a suitable metric subject to a set of requirements. Often such requirements are remarkably complicated, precluding the usage of existing algorithms. For instance, such requirements, referred to as constraints, may necessitate imposing a probabilistic requirement on reliable operation or worst-case adversarial cost. Consequently, addressing such constraints necessitates contending with uncertainty, a lack of linearity (or more specifically nonlinearity), and the presence of kinks in the functional form (alluded to as nonsmoothness). To this end, the project will develop a framework for resolving optimization problems with complex constraints, allowing for capturing the presence of adversarial interactions, the encoding of risk-aversion, and a comprehensive representation of hierarchy. The research plan is aggregated around two distinct avenues. The first relies on solving a sequence of well-posed problems that can be approached by a combination of smoothing (of the kinks), Monte-Carlo sampling, and optimization approaches. The second avenue precludes the usage of derivatives (which are unavailable or challenging to compute); instead, by utilizing approximate Monte-Carlo sampling-enabled evaluations and inexact resolutions, to develop a gradient-free framework for resolving such problems. Collectively, this agenda will lead to the development of expansive tools for optimizing systems with challenging constraints supported by rigorous performance guarantees.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 06, 2025
- Source ID
- FA95502410259
Entities
People
- Vinayak Shanbhag
Organizations
- Air Force Office of Scientific Research
- Board of Regents of the University of Michigan
- United States Air Force