We propose and analyze the convergence of a novel stochastic algorithm for solving monotone inclusions that are sum maximal operator monotone, Lipschitzian operator. The requires only unbiased estimations obtain rate $${\mathcal {O}}(log(n)/n)$$ in expectation strongly case, as well almost sure general case. Furthermore, context application to convex–concave saddle point problems, we derive pri...

In this paper, we investigate several two-parameter weak Orlicz–Hardy martingale spaces generated by the $p$-convex and $q$-concave functions, establish their atomic decomposition theorems. Using decomposition, obtain a sufficient condition for boundedness of sublinear operator defined on spaces. Furthermore, dual are considered.

The log-concave projection is an operator that maps a d-dimensional distribution P to approximating density. It known that, with suitable metrics on the underlying spaces, this continuous, but not uniformly continuous. In work, we prove local uniform continuity result for – in particular, establishing map locally Hölder-(1/4) A matching lower bound verifies exponent cannot be improved. We also ...

Imprecise probability framework is usually dedicated to decision processes. In recent work, we have shown that this framework can also be used to compute an interval-valued signal containing all outputs of processes involving a coherent family of conventional linear filters. This approach is based on a very straightforward extension of the expectation operator involving appropriate concave capa...

We establish variational principles for monotone and maximal bifunctions of Brøndsted-Rockafellar type by using our characterization of bifunction’s maximality in reflexive Banach spaces. As applications, we give an existence result of saddle point for convex-concave function and solve an approximate inclusion governed by a maximal monotone operator.

Starting from the study of the Shepard nonlinear operator of maxprod type in [2], [3], in the recent monograph [4], Open Problem 5.5.4, pp. 324-326, the Baskakov max-prod type operator is introduced and the question of the approximation order by this operator is raised. The aim of this note is to obtain the order of uniform approximation Cω1(f ; 1 √ n ) (with the explicit constant C = 24) of an...

The concepts of L-convex function and M-convex function have recently been introduced by Murota as generalizations of submodular function and base polyhedron, respectively, and discrete separation theorems are established for L-convex/concave functions and for M-convex/concave functions as generalizations of Frank's discrete separation theorem for submodular/supermodular set functions and Edmon...

Dijkstra’s algorithm is a well-known algorithm for the single-source shortest path problem in a directed graph with nonnegative edge length. We discuss Dijkstra’s algorithm from the viewpoint of discrete convex analysis, where the concept of discrete convexity called L-convexity plays a central role. We observe first that the dual of the linear programming (LP) formulation of the shortest path ...