Introductory Lectures on Convex Optimization

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1、IntroductoryLecturesonConvexProgrammingVolumeI:BasiccourseYu.NesterovJuly2,1998ContentsIntroduction51NonlinearProgramming91.1TheWorldofNonlinearOptimization::::::::::::::::::::::91.1.1Generalformulationoftheproblem:::::::::::::::::::91.1.2Performanceofnumeri

2、calmethods:::::::::::::::::::121.1.3Complexityboundsforglobaloptimization:::::::::::::::141.1.4Identitycardsofthefields::::::::::::::::::::::::181.2Localmethodsinunconstrainedminimization:::::::::::::::::201.2.1Relaxationandapproximation::::::::::::::::::::::

3、201.2.2Classesofdifferentiablefunctions::::::::::::::::::::241.2.3Gradientmethod:::::::::::::::::::::::::::::281.2.4Newtonmethod::::::::::::::::::::::::::::::341.3First-ordermethodsinnonlinearoptimization:::::::::::::::::381.3.1GradientmethodandNewtonmethod:W

4、hatisdifferent?::::::381.3.2Conjugategradients:::::::::::::::::::::::::::421.3.3Constrainedminimization::::::::::::::::::::::::462SmoothConvexProgramming512.1MinimizationofSmoothFunctions:::::::::::::::::::::::512.1.1Smoothconvexfunctions:::::::::::::::::::::

5、::::512.1.2LowercomplexityboundsforF1;1(Rn):::::::::::::::::56L2.1.3Stronglyconvexfunctions::::::::::::::::::::::::602.1.4LowercomplexityboundsforS1;1(Rn):::::::::::::::::63¹;L2.1.5GradientMethod:::::::::::::::::::::::::::::652.2OptimalMethods:::::::::::::::

6、::::::::::::::::::672.2.1OptimalMethods:::::::::::::::::::::::::::::672.2.2Convexsets::::::::::::::::::::::::::::::::762.2.3GradientMapping::::::::::::::::::::::::::::802.2.4Minimizationmethodsforsimplesets::::::::::::::::::822.3MinimizationProblemwithSmooth

7、Components:::::::::::::::842.3.1MiniMaxProblem::::::::::::::::::::::::::::842.3.2GradientMapping::::::::::::::::::::::::::::8612CONTENTS2.3.3Minimizationmethodsforminimaxproblem::::::::::::::892.3.4OptimizationwithFunctionalConstraints:::::::::::::::922.3.5C

8、onstrainedminimizationprocess::::::::::::::::::::963NonsmoothConvexProgramming1033.1GeneralConvexFunctions::::::::::::::::::::::::::::1033.1.1MotivationandDefinitions::::::::::::::::::::::::1033.