The Use of Monotone Norms in Epigraphical
نویسنده
چکیده
We introduce and study two operations on functions that may be useful on one hand for computing the distance to an epigraph and, on the other hand, for dealing with constraints in mathematical programming. Both of them involve the concept of monotone norms. A special attention is payed to convex functions.
منابع مشابه
The kernel average for two convex functions and its application to the extension and representation of monotone operators
We provide and analyze a based average for two convex functions, based on a kernel function. It covers several known averages such as the arithmetic average, epigraphical average, and the proximal average. When applied to the Fitzpatrick function and the conjugate of Fitzpatrick function associated with a monotone operator, our average produces an autoconjugate (also known as selfdual Lagrangia...
متن کاملTriangular norms and k-Lipschitz property
Inspired by an open problem of Alsina, Frank and Schweizer, k-Lipschitz t-norms are studied. The k-convexity of continuous monotone functions is introduced. Additive generators of k-Lipschitz tnorms are completely characterized by means of k-convexity. For a given k ∈ [1,∞[ the pointwise infimum A∗k of the class of all k-Lipschitz t-norms is introduced.
متن کاملFrom Matrix to Operator Inequalities
We generalize Löwner’s method for proving that matrix monotone functions are operator monotone. The relation x ≤ y on bounded operators is our model for a definition for C∗-relations of being residually finite dimensional. Our main result is a meta-theorem about theorems involving relations on bounded operators. If we can show there are residually finite dimensional relations involved, and veri...
متن کاملA SYSTEM OF GENERALIZED VARIATIONAL INCLUSIONS INVOLVING G-eta-MONOTONE MAPPINGS
We introduce a new concept of general $G$-$eta$-monotone operator generalizing the general $(H,eta)$-monotone operator cite{arvar2, arvar1}, general $H-$ monotone operator cite{xiahuang} in Banach spaces, and also generalizing $G$-$eta$-monotone operator cite{zhang}, $(A, eta)$-monotone operator cite{verma2}, $A$-monotone operator cite{verma0}, $(H, eta)$-monotone operator cite{fanghuang}...
متن کاملConcavity of Monotone Matrix Functions of Finite Order
Let f : (0; 1) ! R be a monotone matrix function of order n for some arbitrary but xed value of n. We show that f is a matrix concave function of order bn=2c and that kf(A) ? f(B)k kf(jA ? Bj)k for all n-by-n positive semideenite matrices A and B, and all unitarily invariant norms k k. Because f is not assumed to be a monotone matrix function of all orders, Loewner's integral representation of ...
متن کامل