Tuesday, 16:15 - 16:40 h, Room: H 1058

 

Robert Vanderbei
Fast fourier optimization

 

Abstract:
Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. The fast Fourier transform (fft) is a well-known recursive algorithm that can dramatically improve the efficiency for computing the discrete Fourier transform. However, because it is recursive, it is difficult to embed into a linear optimization problem. In this talk, we explain the main idea behind the fast Fourier transform and show how to adapt it so as to make it encodable as constraints in an optimization problem. We demonstrate a real-world problem from the field of high-contrast imaging. On this problem, dramatic improvements are translated to an ability to solve problems with a much finer discretization. As we shall show, in general, the "fast Fourier'' version of the optimization constraints produces a larger but sparser constraint matrix and therefore one can think of the fast Fourier transform as a method of sparsifying the constraints in an optimization problem.

 

Talk 3 of the invited session Tue.3.H 1058
"NLP and MINLP software" [...]
Cluster 10
"Implementations & software" [...]

 

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