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Exhausters and subdifferentials in non-smooth analysis. (English) Zbl 1220.49007
Summary: Non-smooth analysis manifested itself in the 1960s of the last century and is still gaining momentum developing new tools and harnesses and covering new areas of application. One of the notions of non-smooth analysis is that of the exhauster. The exhauster represents a dual construction in nonsmooth analysis. The relationships between upper and lower exhausters and various subdifferentials of non-smooth functions are discussed in this article. It is shown that exhausters are closely related to other non-smooth tools, such as the Michel-Penot, Clarke, Gâteaux and Fréchet subdifferentials. Formulae for computing these subdifferentials by means of exhausters are obtained. The discovered relations are all in the form of equalities, i.e. a calculus for computing the mentioned subdifferentials by means of exhausters is provided.
MSC:
49J52Nonsmooth analysis (other weak concepts of optimality)
49J53Set-valued and variational analysis
26B25Convexity and generalizations (several real variables)
90C46Optimality conditions, duality