We prove that a special variety of quadratically constrained quadratic programs, occurring frequently in conjunction with the design of wave systems obeying causality and passivity (i.e. systems with bounded response), universally exhibit strong duality. Directly, the problem of continuum (grayscale or effective medium) device design for any (complex) quadratic wave objective governed by independent quadratic constraints can be solved as a convex program. The result guarantees that performance limits for many common physical objectives can be made nearly tight, and suggests far-reaching implications for problems in optics, acoustics, and quantum mechanics.
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