Abstract
The chain rule for the subdifferential of a real convex functional composite with an affine operator and a real convex functional is well known (Ekeland-Temam, 1974). Various extensions of this classical case involving operators taking values in an ordered vector space have been considered by many people, for example Lescarret (1968), Levin (1970), Ioffe-Levin (1972), Valadier (1972), Zowe (1974), Penot (1976), Kutateladze (1977), Hiriart-Urruty (1980), Thera (1981) in a convex framework and Thibault (1980) in a non-convex situation.
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Lemaire, B. (1985). Application of a Subdifferential of a Convex Composite Functional to Optimal Control in Variational Inequalities. In: Demyanov, V.F., Pallaschke, D. (eds) Nondifferentiable Optimization: Motivations and Applications. Lecture Notes in Economics and Mathematical Systems, vol 255. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-12603-5_10
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DOI: https://doi.org/10.1007/978-3-662-12603-5_10
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