Topological Aspects of Nonsmooth Optimization

Focusing on nonsmooth structures in optimization, this book explores four key problems: mathematical programs with complementarity constraints, general semi-infinite programming, mathematical programs with vanishing constraints, and bilevel optimization. It employs a topological approach to analyze feasible sets and introduces critical point theory based on Morse's concepts. Additionally, it addresses parametric and stability issues, systematically developing a comprehensive theory applicable to a wide range of optimization problems characterized by nonsmoothness.