ConvexOptimization:Algorithmsand Complexity

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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.

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

  Convexoptimization