Overview
- Authors:
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Diethard Klatte
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Institute for Operations Research and Mathematical Methods of Economics, University of Zurich, Switzerland
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Bernd Kummer
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Institute of Mathematics, Faculty of Mathematics and Natural Sciences II, Humboldt University Berlin, Germany
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Table of contents (12 chapters)
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Front Matter
Pages i-xxviii
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Back Matter
Pages 303-332
About this book
Many questions dealing with solvability, stability and solution methods for va- ational inequalities or equilibrium, optimization and complementarity problems lead to the analysis of certain (perturbed) equations. This often requires a - formulation of the initial model being under consideration. Due to the specific of the original problem, the resulting equation is usually either not differ- tiable (even if the data of the original model are smooth), or it does not satisfy the assumptions of the classical implicit function theorem. This phenomenon is the main reason why a considerable analytical inst- ment dealing with generalized equations (i.e., with finding zeros of multivalued mappings) and nonsmooth equations (i.e., the defining functions are not c- tinuously differentiable) has been developed during the last 20 years, and that under very different viewpoints and assumptions. In this theory, the classical hypotheses of convex analysis, in particular, monotonicity and convexity, have been weakened or dropped, and the scope of possible applications seems to be quite large. Briefly, this discipline is often called nonsmooth analysis, sometimes also variational analysis. Our book fits into this discipline, however, our main intention is to develop the analytical theory in close connection with the needs of applications in optimization and related subjects. Main Topics of the Book 1. Extended analysis of Lipschitz functions and their generalized derivatives, including ”Newton maps” and regularity of multivalued mappings. 2. Principle of successive approximation under metric regularity and its - plication to implicit functions.
Authors and Affiliations
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Institute for Operations Research and Mathematical Methods of Economics, University of Zurich, Switzerland
Diethard Klatte
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Institute of Mathematics, Faculty of Mathematics and Natural Sciences II, Humboldt University Berlin, Germany
Bernd Kummer
