On Continuous Codifferentiability of Quasidifferentiable Functions

Igor M. Prudnikov ()
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Igor M. Prudnikov: Scientific Center of Smolensk Federal Medical University

SN Operations Research Forum, 2021, vol. 2, issue 3, 1-15

Abstract: Abstract The author studied codifferentiable functions introduced by Professor V.F. Demyanov and a method for calculating their subdifferentials and codifferentials. The proven theorems give the rules for calculating the subdifferentials. It was shown that the subdifferential of the first order, introduced by the author, coincides with the Demyanov’s difference applied to the subdifferential and superdifferential of a Lipschitz quasidifferentiable function. The author proved that any quasidifferentiable function is continuously codifferentiable under the condition of upper semicontinuity for the subdifferential and superdifferential mappings. The author suggested constructing a continuous extension for the subdifferential of the first order and introduced $$\alpha$$ α -optimal points.

Keywords: Quasidifferentiable functions; Generalized gradients; Codifferentiable functions; Subdifferential of the first order; The Clarke subdifferential; The Michel-Penot subdifferential; Necessary and sufficient conditions of optimality; Continuous codifferentiability; 49J52; 90C30; 90C31 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s43069-021-00085-w

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