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ConvexOptimization:Algorithmsand Complexity

Foundations and TrendsR in Machine LearningVol. 8, No. 3-4 (2015) 231 357c 2015 S. BubeckDOI: Optimization: Algorithms andComplexityS bastien BubeckTheory Group, Microsoft Some convex optimization problems in machine learning . Basic properties of convexity .. Why convexity? .. Black-box model .. Structured optimization .. Overview of the results and disclaimer ..2402 Convex optimization in finite The center of gravity method .. The ellipsoid method .. Vaidya s cutting plane method .. Conjugate gradient ..2583 Dimension-free convex Projected subgradient descent for Lipschitz functions .. Gradient descent for smooth functions .. Conditional gradient descent, aka Frank-Wolfe .. Strong convexity .. Lower bounds .. Geometric descent .. Nesterov s accelerated gradient descent ..2894 Almost dimension-free convex optimization in Mirror maps .. Mirror descent.

FoundationsandTrendsR inMachineLearning Vol.8,No.3-4(2015)231–357 c 2015S.Bubeck DOI:10.1561/2200000050 ConvexOptimization:Algorithmsand Complexity SébastienBubeck

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