非光滑优化的拓扑方法

PrefaceNotation1 Introduction1．1 Nonsmooth optimization framework1．2 Topological approach1．3 Genericity and stability issues1．4 Nonlinear programming： smooth case2 Mathematical Programming Problems with Complementarity Constraints2．1 Applications and examples2．2 Stability and structure of the feasible set2．2．1 Constraint qualifications MFC and SMFC2．2．2 SMFC implies stability and Lipschitz manifold2．3 Critical point theory2．4 Parametric aspects3 General Semi—infinite Programming Problems3．1 Applications and examples3．2 Structure of the feasible set3．2．1 Closure of the feasible set and Sym—MFCQ3．2．2 Feasible set as a Lipschitz manifold3．3 Nonsmooth symmetric reduction ansatz3．4 Critical point theory4 Mathematical Programming Problems with Vanishing Constraints4．1 Applications and examples4．2 Critical point theory5 Bilevel Optimization5．1 Applications and examples5．2 Five types in parametric optimization5．3 Structure of the feasible set： dim（x） = 15．4 Toward the case dim（x） ≥ 2
6 Impacts on Nonsmooth Analysis6．1 Criticality for nonsmooth functions6．2 Versions of Sard’s Theorem6．3 Regularity and implicit functionsA TopologyA．1 Cell attachment and deformationA．2 Whitney topologyB AnalysisB．1 Manifolds and implicit functionsB．2 TransversalityReferencesIndex