Iteration Semigroups with Generalized Convex, Concave and Affine Elements
نویسندگان
چکیده
Given continuous functions M and N of two variables, it is shown that if in a continuous iteration semigroup with only (M,N)-convex or (M,N)-concave elements there are two (M,N)-affine elements, then M = N and every element of the semigroup is M -affine. Moreover, all functions in the semigroup either are M -convex or M -concave.
منابع مشابه
Decomposition Techniques for Bilinear Saddle Point Problems and Variational Inequalities with Affine Monotone Operators
The majority of First Order methods for large-scale convex-concave saddle point problems and variational inequalities with monotone operators are proximal algorithms which at every iteration need to minimize over problem’s domain X the sum of a linear form and a strongly convex function. To make such an algorithm practical, X should be proximal-friendly – admit a strongly convex function with e...
متن کاملOn the Convergence of Iteration Processes for Semigroups of Nonlinear Mappings in Banach Spaces
Let C be a bounded, closed, convex subset of a uniformly convex Banach space X. We investigate the convergence of the generalized Krasnosel’skiiMann and Ishikawa iteration processes to common fixed points of pointwise Lipschitzian semigroups of nonlinear mappings Tt : C → C. Each of Tt is assumed to be pointwise Lipschitzian, that is, there exists a family of functions αt : C → [0,∞) such that ...
متن کاملHukuhara’s Derivative and Concave Iteration Semigroups of Linear Set-valued Functions
Let K be a closed convex cone with the nonempty interior in a real Banach space and cc(K) denote the family of all nonempty convex compact subsets of K. If {F t : t ≥ 0} is a concave iteration semigroup of continuous linear set-valued functions F t : K → cc(K) with F (x) = {x} for x ∈ K, then DtF (x) = F (G(x)) for x ∈ K and t ≥ 0, where DtF (x) denotes the Hukuhara derivative of F (x) with res...
متن کاملJensen’s Inequality for g-Convex Function under g-Expectation
A real valued function defined on R is called g–convex if it satisfies the following “generalized Jensen’s inequality” under a given g-expectation, i.e., h(E[X ]) ≤ E[h(X)], for all random variables X such that both sides of the inequality are meaningful. In this paper we will give a necessary and sufficient conditions for a C-function being g-convex. We also studied some more general situation...
متن کاملSchool of Economics and Finance A Generalized Endogenous Grid Method for Non-concave Problems
This paper extends Carroll’s (2006) endogenous grid method and its combination with value function iteration by Barillas and Fernández-Villaverde (2007) to nonconcave problems. The method is illustrated using a consumer problem in which consumers choose both durable and non-durable consumption. The durable choice is discrete and subject to non-convex adjustment costs. The algorithm yields subst...
متن کامل