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Fundamental Barriers in Optimisation, Statistics, and Signal Processing

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When solving optimisation problems such as linear programming (LP), semidefinite programming (SDP), basis pursuit (BP), LASSO , or training neural networks, we often discuss algorithms in terms of their ability to achieve an adequately small suboptimality of the objective function. In this talk we ask a different question: Do optimisation algorithms find good approximations to exact optima? We will see that the answer to this question is surprisingly nuanced, with implications for the theory of numerical condition and complexity theory.

This talk is part of the Applied and Computational Analysis series.

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