Linear Programming Algorithms Using Least-Squares Method

To my beloved wife, Yuijn iii ACKNOWLEDGEMENTS First, I want to thank my wife Yujin for her enduring patience and loving support during my study. She has been always there for me from the very beginning to this very end. She has been at the core of my motivation even when I was doubting if could finish this program. I also have to mention my beloved children, Lynn and Olivia, who have been an encouraging reminder that I have a job to complete. I appreciate my parents for the prayer they have done for me morning and night. Not only that, my father managed to continue his financial support even after he had to suffer all the financial loss from his business. It was more than a sacrificial love that the father could give to his son. Special thanks goes to my advisor, Dr. Ellis Johnson. No wonder he amazed me with his creative advice with the depth of his knowledge whenever I had to ask his help in my research. What inspired me most was his personality. His patience has sustained my research no matter how slow my research would seem to progress. He is the best teacher that I could have in my life. I would like to thank Dr. Earl Barnes and Dr. Sokol for reviewing the papers line by line for months, and giving me ideas and helpful advices. I would like to thank Dr. Tetali, who taught me two important math courses, which helped me very much. Dr. Savelsbergh's helpful suggestions made good improvement in the research. I want to express my appreciation to my office mate Kapil, who taught me many programming skills, and spent so much time for discussing my research. I would like to thank Aang, Ethan and Wut, who started Ph.D program with me, and shared and helped in many ways. I also want to express thanks to other ISYE friends for their help. I am indebted to many of the Korean friends in ISYE. Myunsuk and Hyunsuk helped me in many ways in my research. Chuljong helped me when my family had a hard time iv Finally and most importantly, I would like to give thanks to God, who was there with me in my difficult time, is with me, and will be with me. SUMMARY The simplex method is the most widely used algorithm for solving linear programming problems. …