We study the applicability of the Peaceman-Rachford (PR) splitting method for solving nonconvex optimization problems. When applied to minimizing the sum of a strongly convex Lipschitz differentiable function and a proper closed function, we show that if the strongly convex function has a large enough strong convexity modulus and the step-size parameter is chosen below a threshold that is compu...

In this paper, we focus on the application of the Peaceman-Rachford splitting method (PRSM) to a convex minimization model with linear constraints and a separable objective function. Compared to the Douglas-Rachford splitting method (DRSM), another splitting method from which the alternating direction method of multipliers originates, PRSM requires more restrictive assumptions to ensure its con...

Spiritual well-being is perceived to be reflected in the quality of relationships that people have in four areas, namely with God, others, nature, and self. Many spiritual well-being questionnaires exist, but not many provide an adequate assessment of these four relationships. As part of a survey of parental perceptions of holistic early childhood education in kindergartens in Hong Kong, 1383 p...

1. Introduction. A major thrust in current network research involves the development of algorithms for uncovering clusters in network data. Network data come in the form of a graph G = (V, E) where V is a set of vertices and E is a set of unordered pairs of vertices, called edges. All these algorithms seek to partition the vertices in V into m > 1 subsets within which vertex-vertex connections ...