Geodesic
Subdifferentials of Performance Functions and Calculus of Coderivatives of Set-Valued Mappings
Serdica Mathematical Journal, Tome 22 (1996) no. 3, pp. 359-384

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The paper contains calculus rules for coderivatives of compositions, sums and intersections of set-valued mappings. The types of coderivatives considered correspond to Dini-Hadamard and limiting Dini-Hadamard subdifferentials in Gˆateaux differentiable spaces, Fréchet and limiting Fréchet subdifferentials in Asplund spaces and approximate subdifferentials in arbitrary Banach spaces. The key element of the unified approach to obtaining various calculus rules for various types of derivatives presented in the paper are simple formulas for subdifferentials of marginal, or performance functions.
Keywords: Set-Valued Mapping, Lower Semicontinuous Function, Subdifferential, Normal Cone, Coderivative, Marginal Function 
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     author = {Ioffe, Alexander and Penot, Jean-Paul},
     title = {Subdifferentials of {Performance} {Functions} and {Calculus} of {Coderivatives} of {Set-Valued} {Mappings}},
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Ioffe, Alexander; Penot, Jean-Paul. Subdifferentials of Performance Functions and Calculus of Coderivatives of Set-Valued Mappings. Serdica Mathematical Journal, Tome 22 (1996) no. 3, pp. 359-384. http://geodesic.mathdoc.fr/item/SMJ2_1996_22_3_a5/