标题： 纪律凸凹规划 显示英文标题

标题： Disciplined Convex-Concave Programming

摘要： 在本文中，我们引入了纪律凸凹规划（DCCP），它结合了纪律凸规划（DCP）和凸凹规划（CCP）的思想。 凸凹规划是一种用于解决涉及目标函数和约束函数的非凸问题的有组织启发式方法，这些函数是凸项和凹项之和。 DCP 是一种定义凸优化问题的结构化方法，基于一组基本的凸函数和凹函数以及几个组合它们的规则。 使用 DCP 表达的问题可以自动转换为标准形式，并由通用求解器求解；广泛使用的实现包括 YALMIP、CVX、CVXPY 和 Convex.jl。 在本文中，我们提出了一种结合这两种思想的框架，并对先前发表的凸凹规划工作进行了两项改进，特别是处理函数的定义域以及定义域边界上的不可微性问题。 我们描述了一个名为 DCCP 的 Python 实现，它扩展了 CVXPY，并给出了示例。 显示英文摘要

摘要： 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.