No abstract

In this paper we introduce disciplined convex-concave programming (DCCP), which combines the ideas of disciplined convex programming (DCP) with convex-concave programming (CCP). Convex-concave programming is an organized heuristic for solving nonconvex problems that involve objective and constraint functions that are a sum of a convex and a concave term. DCP is a structured way to define convex optimization problems, based on a family of basic convex and concave functions and a few rules for combining them. Problems expressed using DCP can be automatically converted to standard form and solved by a generic solver; widely used implementations include YALMIP, CVX, CVXPY, and Convex.jl. In this paper we propose a framework that combines the two ideas, and includes two improvements over previously published work on convex-concave programming, specifically the handling of domains of the functions, and the issue of nondifferentiability on the boundary of the domains. We describe a Python implementation called DCCP, which extends CVXPY, and give examples.

Linearized alternating direction method of multipliers (ADMM) as an extension of ADMM has been widely used to solve linearly constrained problems in signal processing, machine leaning, communications, and many other fields. Despite its broad applications in nonconvex optimization, for a great number of nonconvex and nonsmooth objective functions, its theoretical convergence guarantee is still an open problem. In this paper, we propose a two-block linearized ADMM and a multi-block parallel linearized ADMM for problems with nonconvex and nonsmooth objectives. Mathematically, we present that the algorithms can converge for a broader class of objective functions under less strict assumptions compared with previous works. Furthermore, our proposed algorithm can update coupled variables in parallel and work for less restrictive nonconvex problems, where the traditional ADMM may have difficulties in solving subproblems.

Background: Newcastle disease (ND) caused by virulent Newcastle disease virus (NDV) is an acute, highly contagious and fatal viral disease affecting most species of birds. Ducks are generally considered to be natural reservoirs or carriers of NDV while being resistant to NDV strains, even those most virulent for chickens; however, natural ND cases in ducks have been gradually increasing in recent years. In the present study, ducks of different breeds and ages were experimentally infected with duck origin virulent NDV strain duck/Jiangsu/JSD0812/2008 (JSD0812) by various routes to investigate the pathogenicity of NDV in ducks.