Geometric Approaches to Near-Optimization
Abstract
The high-level goal of this project is to develop geometrically-motivated algorithms for near optimization, which involves identifying multiple nearly-optimal solutions for variational problems. The motivation here is that objective functions often have shallow regions where many candidate solutions provide reasonable levels of performance. Identifying near-optima helps engineers understand possible trade-offs when selecting a final solution to a problem, can reveal structure in the objective function, and can suggest secondary objective functions to tie-break between nearly indistinguishable points. The algorithms studied in this project are built from geometric theory, understanding the near-optimal region as a shape embedded in a high-dimensional design space. The shape of this region captures the flexibility to adjust the solution to an optimization problem without affecting the objective value significantly.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 21, 2023
- Accession Number
- AD1226757
Entities
Organizations
- Massachusetts Institute of Technology