This book deals with nonsmooth structures arising within the
optimization setting. It considers four optimization problems, namely,
mathematical programs with complementarity constraints, general
semi-infinite programming problems, mathematical programs with vanishing
constraints and bilevel optimization. The author uses the topological
approach and topological invariants of corresponding feasible sets are
investigated. Moreover, the critical point theory in the sense of Morse
is presented and parametric and stability issues are considered. The
material progresses systematically and establishes a comprehensive
theory for a rather broad class of optimization problems tailored to
their particular type of nonsmoothness.
Topological Aspects of Nonsmooth Optimization will benefit researchers
and graduate students in applied mathematics, especially those working
in optimization theory, nonsmooth analysis, algebraic topology and
singularity theory.