The aim of this paper is to study the convexity of the minimizers of some variational problems in Wiener spaces. In the Euclidean setting convexity is a widely discussed issue [25]. Recently, following previous work by Korevaar [26] and Alvarez, Lasry and Lions [2], Alter, Caselles and Chambolle [1, 12] showed the convexity of solutions to variational problems involving functionals with linear ...

Abstract. Let f ∈ C[−1, 1] change its convexity finitely many times, in the interval. We are interested in estimating the degree of approximation of f by polynomials which are coconvex with it, namely, polynomials that change their convexity exactly at the points where f does. We discuss some Jackson type estimates where the constants involved depend on the location of the points of change of c...

We show the convergence of 1+λ-ES with standard step-size update-rules on a large family of fitness functions without any convexity assumption or quasi-convexity assumptions ([5, 6]). The result provides a rule for choosing λ and shows the consistency of halting criteria based on thresholds on the step-size. The family of functions under work is defined through a conditionnumber that generalize...

Let A and B be C∗-algebras. We consider a noncommutative convexity in Hilbert A -B-bimodules, called A -B-convexity, as a generalization of C∗-convexity in C∗-algebras. We show that if X is a Hilbert A -B-bimodule, then Mn(X ) is a Hilbert Mn(A )-Mn(B)-bimodule and apply it to show that the closed unit ball of every Hilbert A -B-bimodule is A -B-convex. Some properties of this kind of convexity...

Borwein, Affleck, and Girgensohn (2000) posed a problem concerning the shape (that is, convexity, log-convexity, reciprocal concavity) of a certain function of several arguments that had manifested in a number of contexts concerned with optimization problems. In this paper we further explore the shape of the Borwein-Affleck-Girgensohn function and especially its extensions generated by complete...