Graph learning has been an active research area that finds applications across a number of fields including finance, health care, and social sciences. In this chapter, we present an overview of recent advancements in the area of learning graphs from data, in particular undirected, weighted graphs...
We propose a Bregman inertial forward-reflected-backward (BiFRB) method for nonconvex composite problems. Assuming the generalized concave Kurdyka-Łojasiewicz property, we obtain sequential convergence of BiFRB, as well as convergence rates on both the function value and actual sequence. One distingu...
Intuitively, recall that any point on the line between two arbitrary points of a convex function will be above that function. In more formal terms, a continuous segment (that is, a straight line) connecting two arbitrary points on the graph of the objective function will not go below the ob...
Authors: Naum Z. Shor Part of the book series: Nonconvex Optimization and Its Applications (NOIA, volume 24) 3 Altmetric This is a preview of subscription content, log in via an institution to check access. About this book Polynomial extremal problems (PEP) constitute one of the most imp...
Peng, B., Wang, L.: An iterative coordinate descent algorithm for high-dimensional nonconvex penalized quantile regression. J. Compu. Graph. Stat. 24 , 676–694 (2015) MathSciNetPeng, B., Wang, L.: An iterative coordinate descent algorithm for high-dimensional nonconvex penalized quantile ...
2. As can be seen, the graph suggests the value function V(x) be convex away from the origin (we set ℓ=1×10−5 in Definition 1.1), evidence that finds support in the result of Theorem 3.1. Download: Download high-res image (88KB) Download: Download full-size image Fig. 2. ...
In [1] some qualitative properties of domains admitting solutions to (1.2) were shown, in particular when Ω is the hypograph of a C2 function v:ω→R, i.e. Ω=Ωv={(x′,xN)∈RN | x′∈ω, xN∈(0,v(x′))}. (1.4) Here ΓΩv is just the cartesian graph of v over ω...
What is a convex non-linear problem? How to show that a set is convex? How to prove convex set? How to check if a function is convex? How to check a function is convex or not? Prove that the following set is not convex. S = \{(x_1, x_2, x_3)\in R^3 | x_1^2 + x...
5. f is concave if and only if it Hipograph: Hipo(f) = { (x, y) ∈ S x R : y ≤ f(x) } is a convex set of Rn+1 Convexity is not a sufficient condition for differentiability, for example the function f(x) = |x| Is not differentiable at x = 0, however it is...
Generally, the rank function is nothing but the l0-norm of the singular values of the image matrix. For cartoon component, we take the advantage of the piecewise constant TV norm and the non-convex function to regularize the texture component. The new decomposition model is defined as ...