graduate texts in mathematics foundation of optimization

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1、Contents1DierentialCalculus:::::::::::::::::::::::::::::::::::::::11.1Taylor'sFormula......................................11.2DierentiationofFunctionsofSeveralVariables...........51.3DierentiabilityofVector-ValuedFunctions...............81.4TheChainRule.......................................101.

2、5Taylor'sFormulaforFunctionsofSeveralVariables........131.6TheConverseofTaylor'sTheorem.......................161.7Danskin'sTheorem....................................201.8Exercises.............................................222UnconstrainedOptimization:::::::::::::::::::::::::::::::312.1BasicResul

3、tsontheExistenceofOptimizers..............322.2First-OrderOptimalityConditions.......................352.3Second-OrderOptimalityConditions.....................372.4QuadraticForms......................................402.5TheInverseFunction,ImplicitFunction,andLyusternikTheoremsinFiniteDimensions....

4、......................442.6Morse'sLemma.......................................482.7SemicontinuousFunctions..............................512.8Exercises.............................................553VariationalPrinciples::::::::::::::::::::::::::::::::::::::613.1Ekeland's-VariationalPrinciple.......

5、.................613.2Borwein{PreissVariationalPrinciple.....................683.3ConsistencyofLinearEqualitiesandInequalities..........713.4VariationalProofsofSomeBasicTheoremsofNonlinearAnalysis..............................................763.5Exercises............................................

6、.82XVIContents4ConvexAnalysis:::::::::::::::::::::::::::::::::::::::::::854.1AneGeometry.......................................854.2ConvexSets..........................................894.3ConvexFunctions.....................................954.4DierentiableConvexFunctions.........................

7、974.5OptimizationonConvexSets...........................1014.6VariationalPrinciplesonaClosedConvexSet.............1064.7Exercises.............................................1075StructureofConvexSetsa