Geometric Optimization and Combinatorial Homological Programming
Technical Report,03 Apr 2018,03 Oct 2019
University of Pennsylvania Philadelphia United States
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New mathematical methods for distributed optimization and related problems were generated using concepts from algebraic topology and sheaf theory. In particular, the Hodge Laplacian was extended to sheaves of data in the context of distributed optimization, indoor mapping, network communications, and learning. The results greatly extend known results from spectral graph theory and simultaneous localization and mapping.
- Theoretical Mathematics