Abstract
We study the conjugate function, the subdifferential, and the ε-subdifferential of a convex function g of the form σ Ω o F, where F is a convex operator from an Euclidean space H into the space S n of n-by-n symmetric matrices, and σ Ω the support function of a convex compact set Ω. of n-by-n symmetric positive semidefinite matrices. Various convex functions defined over a space of symmetric matrices are modeled in such a way. These tools from Convex Analysis serve to analyze the sensitivity of g (X) to perturbations on the variable X ∈ H. In particular, we study in more details the case where F is an affine operator from H into S n.
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© 1992 Springer-Verlag Berlin Heidelberg
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Hiriart-Urruty, JB., Seeger, A., Ye, D. (1992). Sensitivity Analysis for a Class of Convex Functions Defined Over a Space of Symmetric Matrices. In: Oettli, W., Pallaschke, D. (eds) Advances in Optimization. Lecture Notes in Economics and Mathematical Systems, vol 382. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51682-5_10
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DOI: https://doi.org/10.1007/978-3-642-51682-5_10
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