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$\min_{x \in P} f(x)$
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How does optimization shape the world? The majority of decision-making is based off of optimization, from opening google maps to go to our favorite restaurants, to allocating inventory across vast warehouse networks, to regulating energy markets, to training neural networks. Optimization gets it all done. Informally, problems have three aspects: decision variables, constraints, and an objective. Our goal is to find the decision that satisfies the given constraints and which minimizes (or maximizes) the objective function. This in short defines the title of this post: