Generalized Directional Derivatives - Pastor, Karel;Bedna ík, Du an
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Over the last fifty years, generalized second-order derivatives have been studied because it is important to state optimization conditions for nonsmooth functions. We recall e.g. the concept of convex subdifferential, the Clarke gradient for locally Lipschitz function or the co-derivatives studied by Boris Mordukhovich. In this book it was introduced the class of l-stable functions which is wider than the class of functions with locally Lipschitz gradient and there were stated some second-order optimization conditions. The characterization of convexity and strict convexity for locally…mehr

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Produktbeschreibung
Over the last fifty years, generalized second-order derivatives have been studied because it is important to state optimization conditions for nonsmooth functions. We recall e.g. the concept of convex subdifferential, the Clarke gradient for locally Lipschitz function or the co-derivatives studied by Boris Mordukhovich. In this book it was introduced the class of l-stable functions which is wider than the class of functions with locally Lipschitz gradient and there were stated some second-order optimization conditions. The characterization of convexity and strict convexity for locally Licpschitz functions is also provided. Moreover, a new characterization of minimal cusco is given.
Autorenporträt
Karel Pastor; Ph.D.: Studied Mathematical Analysis at Palacký University in Olomouc. Lecturer at Palacký University in Olomouc. Duan Bednäík; Ph.D.: Studied Mathematical Analysis at Palacký University in Olomouc. Lecturer at University of Hradec Králové. Both authors interested in Nonlinear Functional Analysis.