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Pré-Publication, Document De Travail Année : 2008

On the subdifferentiability of the difference of two functions and local minimization

Résumé

We set up a formula for the Fréchet and $\varespilon$-Fréchet subdifferentials of the difference of two convex functions. We even extend it to the difference of two approximately starshaped functions. As a consequence of this formula, we give necessary and sufficient conditions for local optimality in nonconvex optimization. Our analysis relies on the notion of gap continuity of multivalued maps and involves concepts of independent interest such as the notions of blunt and sharp minimizers.
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Dates et versions

hal-00423410 , version 1 (10-10-2009)

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  • HAL Id : hal-00423410 , version 1

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Tijani Amahroq, Jean-Paul Penot, Aïcha Syam. On the subdifferentiability of the difference of two functions and local minimization. 2008. ⟨hal-00423410⟩
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