Topological Aspects of Nonsmooth Optimization (Springer Optimization and Its Applications: Nonconvex Optimization and Its Applications, Vol. 64)

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. ​

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John Hooker is T. Jerome Holleran Professor of Business Ethics and Social Responsibility, and Professor of Operations Research, at Carnegie Mellon University.  He is also part-time Visiting Professor at London School of Economics, 2009-2011.  He holds doctoral degrees in philosophy and management science.  His research interests include operations research, business ethics, and cross-cultural issues.  He teaches courses in these fields at the undergraduate, postgraduate, and executive levels, and he has published over 130 articles and seven books.  He is founding editor-in-chief of the Journal of Business Ethics Education and an area editor for INFORMS Journal on Computing.  He is founding director of the Center for International Corporate Responsibility at Carnegie Mellon.  He was recently named an INFORMS Fellow for outstanding contributions to operations research and the management sciences.  His recent book Integrated Methods for Optimization reflects his primary research interests in operations research.  He developed the ethics curriculum, including course materials, used in CMU’s Tepper School of Business, and he has co-organized four conferences on international corporate responsibility.  His book Working across Cultures is used as a text in cross-cultural business courses at several universities.  He has lived and worked in Australia, China, Denmark, India, Qatar, Turkey, the United States, and Zimbabwe, and has extensive experience in Germany, Mexico, and the United Kingdom.  He has led professional workshops in several countries.  He was head of Carnegie Mellon's undergraduate Business Administration Program 1996-2001.  He reorganized the program, led the design of its curriculum, and received a distinguished service award from the Tepper School for his contributions.  In 2009 he received an Award for Sustained Teaching Excellence in the program.