Important inequalities in convex optimization, proofs and intuition

Many talk about data science and machine learning with enthusiasm, but few know about one of the most important building components behind them – convex optimization. Indeed, nowadays nearly every data science problem will first be transformed into an optimization problem and then solved by standard methods. Convex optimization, albeit basic, is the most important concept in optimization and the starting point of all understanding. If you are an aspiring data scientist, convex optimization is an unavoidable subject that you had better learn sooner than later.

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