Stability theorem and extremum conditions for abnormal problems |
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Authors: | E R Avakov |
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Affiliation: | 1.V.A. Trapeznikov Institute of Control Sciences,Russian Academy of Sciences,Moscow,Russia |
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Abstract: | We prove a generalized inverse function theorem in a neighborhood of a singular point of a mapping. As corollaries to this theorem, we obtain an inverse function theorem, an error bound theorem, and a tangent cone theorem that extend and strengthen the corresponding classical results in the irregular case. Using these corollaries, we establish necessary extremum conditions that are meaningful for abnormal problems. |
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