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almostsuremath.com | ||
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terrytao.wordpress.com
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| | | | | In these notes we quickly review the basics of abstract measure theory and integration theory, which were covered in the previous course but will of course be relied upon in the current course. Th... | |
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terrytao.wordpress.com
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| | | | | Thus far, we have only focused on measure and integration theory in the context of Euclidean spaces $latex {{\bf R}^d}&fg=000000$. Now, we will work in a more abstract and general setting, in w... | |
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www.jeremykun.com
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| | | | | Last time we investigated the naive (which I'll henceforth call "classical") notion of the Fourier transform and its inverse. While the development wasn't quite rigorous, we nevertheless discovered elegant formulas and interesting properties that proved useful in at least solving differential equations. Of course, we wouldn't be following this trail of mathematics if it didn't result in some worthwhile applications to programming. While we'll get there eventually, this primer will take us deeper down the rabbit hole of abstraction. | |
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francisbach.com
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| | | [AI summary] The blog post discusses non-convex quadratic optimization problems and their solutions, including the use of strong duality, semidefinite programming (SDP) relaxations, and efficient algorithms. It highlights the importance of these problems in machine learning and optimization, particularly for non-convex problems where strong duality holds. The post also mentions the equivalence between certain non-convex problems and their convex relaxations, such as SDP, and provides examples of when these relaxations are tight or not. Key concepts include the role of eigenvalues in quadratic optimization, the use of Lagrange multipliers, and the application of methods like Newton-Raphson for solving these problems. The author also acknowledges contributions... | ||
