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AMBIENTUM BIOETHICA BIOLOGIA CHEMIA DIGITALIA DRAMATICA EDUCATIO ARTIS GYMNAST. ENGINEERING EPHEMERIDES EUROPAEA GEOGRAPHIA GEOLOGIA HISTORIA HISTORIA ARTIUM INFORMATICA IURISPRUDENTIA MATHEMATICA MUSICA NEGOTIA OECONOMICA PHILOLOGIA PHILOSOPHIA PHYSICA POLITICA PSYCHOLOGIA-PAEDAGOGIA SOCIOLOGIA THEOLOGIA CATHOLICA THEOLOGIA CATHOLICA LATIN THEOLOGIA GR.-CATH. VARAD THEOLOGIA ORTHODOXA THEOLOGIA REF. TRANSYLVAN
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STUDIA MATHEMATICA - Ediţia nr.3 din 2012 | |||||||
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LOOKING FOR AN EXACT DIFFERENCE FORMULA FOR THE DINI-HADAMARD-LIKE SUBDIFFERENTIAL. Autori: . |
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Rezumat: We use in this paper a new concept of a directional subdifferential, namely the Dini-Hadamard-like e-subdifferential, recently introduced in [29], in order to provide a subdifferential formula for the difference of two directionally approximately starshaped functions (a valuable class of nonsmooth functions, see for instance [32]), under weaker conditions than those presented in [7]. As a consequence, we furnish necessary and sufficient optimality conditions for a nonsmooth optimization problem having the difference of two functions as objective. Mathematics Subject Classification (2010): 26B25, 49J52, 90C56. Keywords: Fréchet e-subdifferential, Dini-Hadamard e-subdifferential, Dini-Hadamard-like e-subdifferential, directionally convergent sequence, sponge, directional lower limit, approximately starshaped functions, directionally approximately starshaped functions, spongiously local blunt minimizer. |
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