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Some applications of convex optimizations (ru)
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Intro to numerical optimization methods. Gradient descent (ru)
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How to accelerate gradient descent: conjugate gradient method, heavy-ball method and fast gradient method (vol 1, ru; vol 2, ru)
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Second order methods: Newton method. Quasi-Newton methods as trade-off between convergence speed and cost of one iterations (ru)
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Non-smooth optimization problems: subgradient methods and intro to proximal methods (en)
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Smoothing: smooth minimization of non-smooth functions (original paper) (ru)
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Simple constrained optimization problems: projected gradient method and Frank-Wolfe method (ru)
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General purpose solvers: interior point methods (ru)
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How to parallelize optimization methods: penalty method, augmented Lagrangian method and ADMM (ru)
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Coordinate-wise methods