The DC (Difference of Convex Functions) Programming and DCA Revisited with DC Models of Real World Nonconvex Optimization Problems

By Hoai An Le Thi, Tao Pham Dinh. Annals of Operations Research, 2005

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Visualizing data as objects by DC (difference of convex) optimization (2017, methodology): “We have shown that some convenient choices of Ω (a rectangle or a disc) and B (a disc) yield a closed formula for the optimal solution of the subproblems to be addressed at each stage of the inner DCA, thus avoiding the need of using numerical optimization routines.”
Hinge-Loss Markov Random Fields and Probabilistic Soft Logic (2015, methodology): “For interior ground truth values, we use the difference of convex functions algorithm (An and Tao, 2005) to find a local optimum.”
Federated Learning in Mobile Edge Networks: A Comprehensive Survey (2019, methodology): “Due to the nonconvexity of the mean-square-error constraint and intractability of the optimization problem, a difference-ofconvex functions (DC) algorithm [132] is proposed to solve the maximization problem.”
Hinge-Loss Markov Random Fields and Probabilistic Soft Logic (2015, methodology): “In this case, we use the difference of convex functions algorithm (An and Tao, 2005) to find a local optimum.”
Supervised classification and mathematical optimization (2013, background): “CCCP, a primal variant of the primal-dual DCA of [3], optimizes a series of convex overestimates of the objective, obtained by linearizing one of the terms in its decomposition as difference of two convex functions.”