DC programming and DCA: thirty years of developments

The year 2015 marks the 30th birthday of DC (Difference of Convex functions) programming and DCA (DC Algorithms) which constitute the backbone of nonconvex programming and global optimization. In this article we offer a short survey on thirty years of developments of these theoretical and algorithmi...

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Published inMathematical programming Vol. 169; no. 1; pp. 5 - 68
Main Authors Le Thi, Hoai An, Pham Dinh, Tao
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2018
Springer Nature B.V
Springer Verlag
Subjects
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Computer Science
Full Length Paper
Global optimization
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Mathematics of Computing
Nonlinear programming
Numerical Analysis
Programming
Solvers
Theoretical
DCA
Algorithms
Applications
Theory
DC programming
90C90
90C26
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Summary:The year 2015 marks the 30th birthday of DC (Difference of Convex functions) programming and DCA (DC Algorithms) which constitute the backbone of nonconvex programming and global optimization. In this article we offer a short survey on thirty years of developments of these theoretical and algorithmic tools. The survey is comprised of three parts. In the first part we present a brief history of the field, while in the second we summarize the state-of-the-art results and recent advances. We focus on main theoretical results and DCA solvers for important classes of difficult nonconvex optimization problems, and then give an overview of real-world applications whose solution methods are based on DCA. The third part is devoted to new trends and important open issues, as well as suggestions for future developments.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-018-1235-y