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arXiv · 2105.02154

On Sion's Minimax Theorem, Compact QCQPs, and Wave Scattering Optimization

Sean Molesky·Pengning Chao·Alejandro W. Rodriguez
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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.

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Sean Molesky, Pengning Chao, Alejandro W. Rodriguez. 2021-05-05. On Sion's Minimax Theorem, Compact QCQPs, and Wave Scattering Optimization. https://arxiv.org/abs/2105.02154

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