DC Programming: Overview

By R. Horst, N. Thoai. 1999

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Citations in the corpus

All Models are Wrong, but Many are Useful: Learning a Variable’s Importance by Studying an Entire Class of Prediction Models Simultaneously (2018, background): “Although precise solutions to DC problems are not always tractable, lower bounds can be attained by branch-and-bound (B&B) methods (Horst and Thoai, 1999).”
Incremental Majorization-Minimization Optimization with Application to Large-Scale Machine Learning (2014, methodology): “Such a surrogate appears in DC programming [30].”
Learning with Submodular Functions: A Convex Optimization Perspective (2011, background): “In regular continuous optimization, differences of convex functions play an important role, and appear in various disguises, such as DC-programming [102], concave-convex proce-”
Global Optimization in Geometry — Circle Packing into the Square (2005, background): “Circle Packing into the Square 5 This problem can be considered in the following ways: a) as a DC programming problem Horst and Thoai (1999): A DC (difference of convex functions) programming problem is a mathematical programming problem, where the objective function can be described by a…”
The DC (Difference of Convex Functions) Programming and DCA Revisited with DC Models of Real World Nonconvex Optimization Problems (2005, background): “…solutions to nonconvex programs) whose main tools and solution methods are developed according to the spirit of the combinatorial optimization, but with the difference that one works in the continuous framework (see Horst and Tuy, 1996; Horst, Pardalos, and Thoai, 1995; Horst and Thoai, 1999).”
Variations and extension of the convex–concave procedure (2016, background): “Good overviews of the work that has been done in solving DC programs globally can be found in (Horst and Thoai, 1999; Horst et al, 1995), and the references therein.”
All Models are Wrong but many are Useful: Variable Importance for Black-Box, Proprietary, or Misspecified Prediction Models, using Model Class Reliance (2018, unknown): “constraint function, k2R1, and g DC, h DC, and c DC are convex. Although precise solutions to DC problems are not always tractable, lower bounds can be attained by branch-and-bound (B&B) methods (Horst and Thoai, 1999). A simple B&B approach is to partition into a set of simplexes. Within th”
A Proof of Convergence of the Concave-Convex Procedure Using Zangwill's Theory (2012, unknown): “…such general d.c. programs (see equation 4.3) whose convergence properties are summarized in section 2.6 Let us consider a general d.c. program (Horst & Thoai, 1999), given by min x { u0(x) − v0(x) : ui(x) − vi(x) ≤ 0, i ∈ [m] } , (4.3) where {ui}mi=0, {vi}mi=0 are real-valued continuous…”
Multiple-source adaptation theory and algorithms (2020, methodology): “Note that the global minimum of our DC-programming problem can also be found using a cutting plane method of Horst and Thoai [31] that does not admit known algorithmic convergence guarantees, or a branch-and-bound with exponential convergence [31].”
Majorization-Minimization Algorithms in Signal Processing, Communications, and Machine Learning (2017, unknown): “,m are convex functions [97], [98].”
Disciplined convex-concave programming (2016, background): “Good overviews of solving DC programs globally can be found in [19], [20] and the references therein.”
Batched Stochastic Bayesian Optimization via Combinatorial Constraints Design (2019, unknown): “Lemma 7 (Horst & Thoai (1999)).”