bv_cvxbook_extra_exercises

Formulate the problem maximize pt x subject to probpt

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Unformatted text preview: constraints.) The problem data are F , g , G, α, βi , σi . If you change variables, or transform your problem in any way that is not obvious (for example, you form a relaxation), you must explain fully how your method works, and why it gives the solution. If your method relies on any convex functions that we have not encountered before, you must show that the functions are convex. Disclaimer. The teaching staff does not endorse jamming, optimal or otherwise. 12.10 2D filter design. A symmetric convolution kernel with support {−(N − 1), . . . , N − 1}2 is characterized by N 2 coefficients hkl , k, l = 1, . . . , N. These coefficients will be our variables. The corresponding 2D frequency response (Fourier transform) H : R2 → R is given by H ( ω 1 , ω2 ) = k,l=1,...,N hkl cos((k − 1)ω1 ) cos((l − 1)ω2 ), where ω1 and ω2 are the frequency variables. Evidently we only need to specify H over the region [0, π ]2 , although it is often plotted over the region [−π, π ]2 . (It won’t matter in this problem, but we should mention that the coe...
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