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PrefaceNotation1 Introduction1£®1 Nonsmooth optimization framework1£®2 Topological approach1£®3 Genericity and stability issues1£®4 Nonlinear programming£º 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¡ªinfinite Programming Problems3£®1 Applications and examples3£®2 Structure of the feasible set3£®2£®1 Closure of the feasible set and Sym¡ªMFCQ3£®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£º dim£¨x£© = 15£®4 Toward the case dim£¨x£© ¡Ý 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