Surrogate dual search in nonlinear integer programming.

Wang, Chongyu.Thesis (M.Phil.)--Chinese University of Hong Kong, 2009.Includes bibliographical references (leaves 74-78).Abstract also in Chinese.Abstract --- p.1Abstract in Chinese --- p.3Acknowledgement --- p.4Contents --- p.5List of Tables --- p.7List of Figures --- p.8Chapter 1. --- Introduction --- p.9Chapter 2. --- Conventional Dynamic Programming --- p.15Chapter 2.1. --- Principle of optimality and decomposition --- p.15Chapter 2.2. --- Backward dynamic programming --- p.17Chapter 2.3. --- Forward dynamic programming --- p.20Chapter 2.4. --- Curse of dimensionality --- p.23Chapter 3. --- Surrogate Constraint Formulation --- p.26Chapter 3.1. --- Surrogate constraint formulation --- p.26Chapter 3.2. --- Singly constrained dynamic programming --- p.28Chapter 3.3. --- Surrogate dual search --- p.29Chapter 4. --- Distance Confined Path Algorithm --- p.34Chapter 4.1. --- Yen´ةs algorithm for the kth shortest path problem --- p.35Chapter 4.2. --- Application of Yen´ةs method to integer programming --- p.36Chapter 4.3. --- Distance confined path problem --- p.42Chapter 4.4. --- Application of distance confined path formulation to integer programming --- p.50Chapter 5. --- Convergent Surrogate Dual Search --- p.59Chapter 5.1. --- Algorithm for convergent surrogate dual search --- p.62Chapter 5.2. --- "Solution schemes for (Pμ{αk,αβ)) and f(x) = αk" --- p.63Chapter 5.3. --- Computational Results and Analysis --- p.68Chapter 6. --- Conclusions --- p.72Bibliography --- p.7