Topological Aspects of Nonsmooth Optimization [Hardcover]

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.

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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. 

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.

From the reviews:

This monograph & provides detailed topological investigations of nonsmooth optimization problems. & the book highlights and motivates recent developments in a broad field of active research. The material is well presented, so that the book may be warmly recommended to graduate students and researchers in optimization. (Oliver Stein, Mathematical Reviews, October, 2013)

The textbook (PhD thesis of the author) deals with mathematical programming problems which have smooth data but show, because of their structure, intrinsic non-smooth behavior & . It can bels¢