Convex sets; Convex functions; Optimization problem; Descending gradient method; Subgradient method; Newton's method; Linear and quadratic programming; Duality; Optimality conditions of Karush-Kuhn-Tucker. Interior point methods; Coordinate descent; Conjugated gradient; Trust region; Stochastic descending gradient. Applications in statistics and machine learning problems.
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- Izmailov, Alexey, and Mikhail Solodov. Optimization, Volume 1: Optimality Conditions, Elements of Convex and Duality Analysis. IMPA. 2009.
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- Bubeck, Sébastien. "Convex optimization: Algorithms and complexity." Foundations and Trends® in Machine Learning 8.3-4 (2015): 231-357.