Tim Davidson
Enriching the art of engineering design via convex optimization
EURASIP Seminar presented at SPAWC 2010, Marrakech, Morocco, June 2010.
One of the key steps in engineering design is the choice of the values for the parameters in a chosen configuration of the design. To perform this step effectively, the designer must make judicious trade-offs between competing characteristics of the configuration, or show that no appropriate parameter values exist for the current configuration. Over time, individual disciplines have distilled design experience into sets of guidelines for making these tradeoffs in certain classes of design problems, and these guidelines often yield reasonable designs. The goal of this seminar is to draw attention to the way in which the perspective provided optimization in general, and convex optimization in particular, can enrich the process of making design trade-offs. When the design problem is convex in the parameters, the inherent trade-offs of the configuration - the tradeoffs that cannot be exceeded by any design method - can be reliably obtained, often with little programming effort. The availability of these inherent trade-offs not only enhances the designer's judgement, but also offers the possibility to embed the parameter design procedure in a broader, unsupervised, system. Making judicious trade-offs is substantially more difficult if one or more of the characteristics of the configuration is not convex in the parameters, and in that case the designer's judgement usually plays an even greater role in the design process. However, convex optimization can also enhance that judgement in several ways, including: the provision of inner and outer bounds on the inherent trade-offs, which can be used to evaluate locally optimal solutions; the development of convex local approximations of the design problem for use in sequential approximation algorithms; the provision of starting points for such algorithms; and the development of bounds for use in branch-and-bound algorithms for globally optimal solutions.
The goal of this seminar is to provide an introduction to convex optimization in the context of engineering design, with an emphasis on applications in the areas of signal processing and wireless communications. No previous exposure to convex optimization will be required, but it is hoped that the emphasis on the design process will provide a fresh perspective for those who have already had some exposure.
A pdf file containing an updated version of the slides, in "handout" format, is available here.
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