Disciplined convex-concave programming

By Xinyue Shen, Steven Diamond, Yuantao Gu, Stephen P. Boyd. 2016

179 citations recorded by the source corpus.

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 subdifferentiability on the boundary of the domains. We describe a Python implementation called DCCP, which extends CVXPY, and give examples.

Subfields: Computational Mechanics, Numerical Analysis

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Citations in the corpus

Fairness Beyond Disparate Treatment & Disparate Impact: Learning Classification without Disparate Mistreatment (2016, neutral): “Similarly, depending on the application”
From Parity to Preference-based Notions of Fairness in Classification (2017, methodology): “which, for any convex regularizer ⌦(·), is a disciplined convex-concave program (DCCP) and thus can be efficiently solved using well-known heuristics [30].”
Learning Fair Classifiers: A Regularization-Inspired Approach (2017, methodology): “They then apply well-known heuristics [18] to solve the resulting optimization problem for a convex loss function.”
Penalizing Unfairness in Binary Classification (2017, background): “They then heuristically solve (Shen et al., 2016) the resulting optimization problem for a convex loss function.”
Polyhedral approximation in mixed-integer convex optimization (2016, background): “The full set of DCP rules is reviewed in [23,40].”
Fairness Constraints: A Flexible Approach for Fair Classification (2019, background): “As we later discuss in Section 2, the same notions are often referred to by different names by different studies. ods (Boyd and Vandenberghe, 2004; Shen et al., 2016).”