A GENERAL FRAMEWORK FOR STRUCTURE DECOMPOSITION IN HIGH-DIMENSIONAL PROBLEMS

To my parents Acknowledgements First and foremost, I would like to express my sincerest thanks to Professor Sun De-feng and Professor Xu Huan, my research supervisors, for their professional guidance and generous support throughout my time as their student. Professor Sun, my main supervisor, has provided me with an excellent atmo-sphere for my study and research in optimization. His invaluable advice and in-sightful questions inspire me a lot. And I am deeply impressed by his immense knowledge, rigorous attitude and strong sense of responsibility in academic research. Most importantly, his encouragements have been a great support, inspiring me to go ahead when times were tough. I am truly grateful for his concern about my personal and academic development. As my second supervisor, Professor Xu has been very supportive and has offered valuable and constructive suggestions in the way of the planning and development of this research work. I have benefited a lot from his patient guidance, scientifi