Sensitivity Analysis for a Class of Convex Functions Defined Over a Space of Symmetric Matrices

Abstract

We study the conjugate function, the subdifferential, and the e-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.