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A covering theorem for set-valued mappings |
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| Abstract: | The notion of covering is introduced for a set-valued mapping defined on an arbitrary set in a Banach space. A necessary and sufficient covering criterion is proved. The conditions are formulated in terms of generalized differentials and generalized normals. The covering theorem is applied to deduce formulas of generalized differential calculus and necessary optimality conditions for nonsroooth optimization problems. |
| Keywords: | Nonsmooth analysis generalized differentials set-valued mappings optimality conditions Lagrange multipliers |