Topological Aspects of Nonsmooth Optimization [electronic resource] / by Vladimir Shikhman.

Preface. -Notation -- Introduction -- Mathematical Programming Problems with Complementarity -- Constraints -- General Semi-infinite Programming Problems -- Mathematical Programming Problems with Vanishing Constraints -- Bilevel Optimization -- Impacts on Nonsmooth Analysis -- Appendix -- Bibliography -- References -- Index.

This bookdeals withnonsmooth 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 andbilevel optimization. The author uses thetopologicalapproachand 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 andestablishesacomprehensive theory for a rather broad class of optimization problems tailored to theirparticular type of nonsmoothness. Topological Aspects of Nonsmooth Optimization will benefit researchers and graduate studentsin applied mathematics, especially those workingin optimization theory, nonsmooth analysis, algebraic topology and singularity theory.

ZDB-2-SMA