Topological Aspects of Nonsmooth Optimization

Linking singularity and transversality theory with non-smooth optimization, this book examines complementarity-constrained mathematical programs, semi-infinite programming problems, mathematical programs with vanishing constraints, and bi-level optimization.

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.

Establishes a comprehensive theory for a rather broad class of optimization problems tailored to their particular type of nonsmoothness Considers four optimization problems and uses a topological approach ? Handles various equilibrium optimization problems from the same topological point of view Links ideas from singularity and transversality theory with nonsmooth optimization Includes supplementary material: sn.pub/extras

Contenu

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.