On Sion's Minimax Theorem, Compact QCQPs, and Wave Scattering Optimization
Optimization and Control
2022-03-04 v3 Mathematical Physics
math.MP
Abstract
In these notes, we examine certain implications of Sion's minimax theorem for compact quadratically constrained quadratic programs (QCQPs), particularly QCQPs arising in the context of optimizing wave scattering, in relation to Lagrangian duality. The discussion puts forward an alternative "dual" understanding of optimization for wave phenomena that anticipates the realization of algorithmic (inverse design) methods attaining a guaranteed degree of global optimality for common figures of merit appearing in applied photonics, acoustics, and quantum mechanics.
Cite
@article{arxiv.2105.02154,
title = {On Sion's Minimax Theorem, Compact QCQPs, and Wave Scattering Optimization},
author = {Sean Molesky and Pengning Chao and Alejandro W. Rodriguez},
journal= {arXiv preprint arXiv:2105.02154},
year = {2022}
}
Comments
23 pages, 1 figure