Convex analysis approach to d.c. programming: Theory, Algorithm and Applications

By Tao Pham Dinh, Hoai An Le Thi. 1997

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Citations in the corpus

Multiple-Source Adaptation with Domain Classifiers (2020, background): “Problem (7) can be solved by the DC (difference-of-convex) algorithm [Tao and An, 1997, 1998, Sriperumbudur and Lanckriet, 2012].”
Algorithms and Theory for Multiple-Source Adaptation (2018, background): “Our DC decompositions prove that the optimization problem (4) can be cast as the following variational form of a DC-programming problem [Tao and An, 1997, 1998, Sriperumbudur and Lanckriet, 2012]: The DC-programming algorithm works as follows.”
Partially linear additive quantile regression in ultra-high dimension (2016, methodology): “…estimator for ultra-high dimensional partially linear additive quantile regression model, we explore the necessary condition for the local minimizer of a convex differencing problem [Tao and An (1997); Wang, Wu and Li (2012)] and extend it to the setting involving nonparametric components.”
Robust Active Label Correction (2018, background): “(7), however, suggests that future work might employ DC programming by interpreting it as a difference of two convex functions (Tao, 1997).”
On the Convergence of the Concave-Convex Procedure (2009, methodology): “programming literature, Pham Dinh and Hoai An [8] proposed a primal-dual subdifferential method called DCA (d.”
Infrared Small Target Detection via Non-Convex Rank Approximation Minimization Joint l2, 1 Norm (2018, methodology): “The existing single-frame-based detection algorithms mainly fall into three main groups: methods of background-based assumption, methods of target-based assumption, and methods of target and background separating.”
Minimization of ℓ1-2 for Compressed Sensing (2015, methodology): “The DCA in general does not guarantee a global minimum due to non-convex nature of the problem [45].”
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.”
Multiple-source adaptation theory and algorithms (2020, background): “Our DC decompositions prove that the optimization problem (12) can be cast as the following variational form of a DC-programming problem [53, 56, 57]:”
Qualitative properties of the minimum sum-of-squares clustering problem (2018, background): “, [15] and [27]), which can be considered as a consequence of the optimality condition obtained by Dem’yanov et al.”
Support points (2016, background): “programming methods, which enjoy a well-established theoretical and numerical framework [71, 69].”