《非光滑优化的拓扑方法（英文版）》主要关注了4类优化问题，即带有互补约束的数学问题、一般的半无限优化问题、无约束和双层优化的数学问题。作者采用了拓扑方法，并对相关可行集上的拓扑不变量进行了研究。此外书中还讲述了莫尔斯意义下的临界点理论，并且考虑了其参数和稳定因素。
《非光滑优化的拓扑方法（英文版）》凝聚了作者多年科研和教学成果，适用于科研工作者、高校教师和研究生。
Preface
Notation
1 Introduction
1．1 Nonsmooth optimization framework
1．2 Topological approach
1．3 Genericity and stability issues
1．4 Nonlinear programming： smooth case
2 Mathematical Programming Problems with Complementarity Constraints
2．1 Applications and examples
2．2 Stability and structure of the feasible set
2．2．1 Constraint qualifications MFC and SMFC
2．2．2 SMFC implies stability and Lipschitz manifold
2．3 Critical point theory
2．4 Parametric aspects
3 General Semi—infinite Programming Problems
3．1 Applications and examples
3．2 Structure of the feasible set
3．2．1 Closure of the feasible set and Sym—MFCQ
3．2．2 Feasible set as a Lipschitz manifold
3．3 Nonsmooth symmetric reduction ansatz
3．4 Critical point theory
4 Mathematical Programming Problems with Vanishing Constraints
4．1 Applications and examples
4．2 Critical point theory
5 Bilevel Optimization
5．1 Applications and examples
5．2 Five types in parametric optimization
5．3 Structure of the feasible set： dim（x） = 1
5．4 Toward the case dim（x） ≥ 2
6 Impacts on Nonsmooth Analysis
6．1 Criticality for nonsmooth functions
6．2 Versions of Sards Theorem
6．3 Regularity and implicit functions
A Topology
A．1 Cell attachment and deformation
A．2 Whitney topology
B Analysis
B．1 Manifolds and implicit functions
B．2 Transversality
References
Index
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