Plenary Lecture

DC Programming and DCA - Theory, Algorithms and Applications

Professor Le Thi Hoai An
Laboratory of Theoretical and Applied Computer Science (LITA)
University of Lorraine

Abstract: DC (Difference of Convex functions) Programming and DCA (DC Algorithms), which constitute the backbone of Nonconvex Programming and Global Optimization, were introduced by Pham Dinh Tao in their preliminary form in 1985 and extensively developed by Le Thi Hoai An and Pham Dinh Tao since 1994. (see for example
DC Programming is a natural and logical extension of Convex Programming, sufficiently large to cover almost all nonconvex programs but not too in order to use the powerful arsenal of modern Convex Analysis and Convex Optimization. Note that most real world nonconvex programs are DC programs, and with appropriate DC decompositions, DCA permit to recover, as special cases, most standard algorithms in Convex/Noncovex Programming.
These theoretical and algorithmic tools have been successfully used by many researchers and practitioners to model and solve their nonconvex programs in different fields of Applied Sciences, in particular : Transport-Logistics, Telecommunication, Bioinformatics, Finance, Data Mining and Machine Learning, Cryptology, Mechanics, Image Processing, Robotics & Computer Vision, Petrochemistry, Optimal Control, Inverse Problems and Ill-Posed Problems, Multiobjective Programming, Multilevel Programming, Variational Inequalty Problems (VIP), Mathematical Programs with Equilibrium Constraints (MPEC), etc. Their popularity resides in their robustness and performance compared to existing methods, their adaptation to speciļ¬c structures of addressed problems and their ability to solve real-world large-scale nonconvex programs.
This talk on DC programming and DCA will be comprised of three parts. First we outline basic theoretical and algorithmic tools for an easy understanding of the DC Programming and DCA’s philosophy, while in the second part we show how to solve several classes of hard problems in Combinatorial Optimization and Operations Research by DC Programming and DCA. The third one is devoted to applications of these theoretical and algorithmic tools to the modelling and solution of some real world nonconvex programs in Machine Learning, Finance, Transport-Logistic and Supply Chain Management.

Brief Biography of the Speaker: Prof Le Thi Hoai An obtained his PhD with Distinction in Optimization in 1994, his Habilitation in 1997 from university of Rouen, France. She is currently Director of Laboratory of Theoretical & Applied Computer Science, university of Lorraine and serving as Exceptional Class Professor. She is the author/co-author of more than 220 journal articles, international conference papers and book chapters, the co-editor of 6 books and 12 special issues of international journals, and supervisor of 30 PhD theses. She is Chair of Scientific Committee and Chair of Organizing Committee as well as member of Scientific Committee of numerous International Conferences, and leader of several regional/national/international projects. Her research interests include Numerical Analysis, Optimization and Operations Research and their applications in Information Systems and Industrial Complex Systems in various fields such as, Data Mining and Machine Learning, Telecommunication, Transportation, Supply Chain and Management, Finance, Bioinformatics, Image Analysis, Cryptology, Security & Reliability. She is the co-founder (with Pham Dinh Tao) of DC programming and DCA, an innovative approach in nonconvex programming.

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