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...
In Assumption1, the regularizerhcan be any nonsmooth and nonconvex function so long as it is a closed function. This covers most of the regularizers that we use in practice, including any proper convex functions (can be nonsmooth, e.g.,ℓnorm),ℓnorm with(can be nonconvex and nonsmoo...
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...
whereλandγare nonnegative parameters, andPλ,γ(|ui|) is a non-convex function. We absorbλinto the penalty because it cannot be decoupled from several penalties, such as the SCAD function38. We here have seven penalties and they are described in Table1and visualized in Fig.1, where f...
In this paper, the problem of online distributed optimization with stochastic and nonconvex objective functions is studied by employing a multi-agent system. When making decisions, each agent only has access to a noisy gradient of its own objective function in the previous time and can only commu...
We consider an expected utility maximization problem where the utility function is not necessarily concave and the time horizon is uncertain. We establish
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 ...
Quantum channelNon-commutative graphSandwich theoremLovasz numberWe define non-commutative versions of the vertex packing polytope, the theta convex body and ... Boreland, G.Todorov, I. G.Winter, A. - 《Journal of Combinatorial Theory》 被引量: 0发表: 2021年 Quantum Graphs as Quantum Relations...
It is challenging to directly find the optimal solution of the CHLNMF model since its objective function is non-convex. Therefore, using Semi-quadratic programming theory to solve the objective functionO_{CHLNMF}to find the optimal solution. The primary concept is to add an auxiliary variable an...
Let f : Rp → R be a µ-strongly convex function and Θ ⊆ Rp be a convex set. Let θ⋆ be the minimizer of f on Θ. Then, the following condition holds for all θ in Θ: f (θ) ≥ f (θ⋆) + µ 2 θ − θ⋆ 22. We now introduce a sequence of ...