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Doctoral Dissertation Mathematics: DC algorithms in nonconvex quadratic programming and applications in data clustering

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The dissertation has four chapters: Chapter 1 - Background Materials; Chapter 2 - Analysis of an Algorithm in Indefinite Quadratic Programming; Chapter 3 - Qualitative Properties of the Minimum Sum-of-Squares Clustering Problem; Chapter 4 - Some Incremental Algorithms for the Clustering Problem. | MINISTRY OF EDUCATION AND TRAINING MINISTRY OF NATIONAL DEFENCE MILITARY TECHNICAL ACADEMY TRAN HUNG CUONG DC ALGORITHMS IN NONCONVEX QUADRATIC PROGRAMMING AND APPLICATIONS IN DATA CLUSTERING DOCTORAL DISSERTATION MATHEMATICS HANOI - 2021 MINISTRY OF EDUCATION AND TRAINING MINISTRY OF NATIONAL DEFENCE MILITARY TECHNICAL ACADEMY TRAN HUNG CUONG DC ALGORITHMS IN NONCONVEX QUADRATIC PROGRAMMING AND APPLICATIONS IN DATA CLUSTERING DOCTORAL DISSERTATION Major Mathematical Foundations for Informatics Code 9 46 01 10 RESEARCH SUPERVISIORS 1. Prof. Dr.Sc. Nguyen Dong Yen 2. Prof. Dr.Sc. Pham The Long HANOI - 2021 Confirmation This dissertation was written on the basis of my research works carried out at the Military Technical Academy under the guidance of Prof. Nguyen Dong Yen and Prof. Pham The Long. All the results presented in this dissertation have got agreements of my coauthors to be used here. February 25 2021 The author Tran Hung Cuong i Acknowledgments I would like to express my deep gratitude to my advisor Professor Nguyen Dong Yen and Professor Pham The Long for their careful and effective guid- ance. I would like to thank the board of directors of Military Technical Academy for providing me with pleasant working conditions. I am grateful to the leaders of Hanoi University of Industry the Faculty of Information Technology and my colleagues for granting me various financial supports and or constant help during the three years of my PhD study. I am sincerely grateful to Prof. Jen-Chih Yao from Department of Applied Mathematics National Sun Yat-sen University Taiwan and Prof. Ching- Feng Wen from Research Center for Nonlinear Analysis and Optimization Kaohsiung Medical University Taiwan for granting several short-termed scholarships for my doctorate studies. I would like to thank the following experts for their careful readings of this dissertation and for many useful suggestions which have helped me to improve the presentation Prof. Dang Quang A Prof. Pham Ky Anh