2021/05/05 by Sean Molesky, Molesky, Sean, Pengning Chao +3
Computer Science · Mathematics · #49-02 #78-10 #Advanced Optimization Algorithms Research #Digital Filter Design and Implementation #FOS: Mathematics #FOS: Physical sciences #J.2 #Mathematical Physics (math-ph) #Numerical Methods and Algorithms #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2105.02154
openalex publication_date 2021/05/05 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
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.