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Francis Bach

There are a few mathematical results that any researcher in applied mathematics uses on a daily basis. One of them is Jensen’s inequality, which allows bounding expectations of functions of random variables. This really happens a lot in any probabilistic arguments but also as a tool to generate inequalities and optimization algorithms. In this blog…

Among continuous optimization problems, convex problems (with convex objectives and convex constraints) define a class that can be solved efficiently with a variety of algorithms and with arbitrary precision. This is not true more generally when the convexity assumption is removed (see this post). This of course does not mean that (1) nobody should attempt…

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