In this article, we introduce a convex combination-based distributed momentum method (CDM) for solving distributed optimization to minimize a sum of smooth and strongly convex local objective ...

1. Introduction. The inequalities, (1.1) which discovered by C. Hermite and Hadamard for all convex functions are known in the literature as Hermite-Hadamard inequalities.. We note that ...

A python implementation of the algorithm used to generate optimal piecewise linear approximations of convex functions proposed by Imamoto and Tang .The algorithm uses an iterative search to find the ...

Convex Function: A function defined on an interval or convex set such that the line segment between any two points on its graph lies above or on the graph, a property that is crucial for deriving ...

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Definition 1.3 ([2]). Let A function is said to be s-convex in the second sense if. for all and. If is a convex function on with and, Then we have Hermite-Hardamard’s inequality. (1.1) ...

This work studies the denoising of piecewise smooth graph signals that exhibit inhomogeneous levels of smoothness over a graph, where the value at each node can be vector-valued. We extend the graph ...