Nonlinear and Dynamic Programming : An Introduction

I. Linear and Nonlinear Programming -- II. Elements of the Mathematical Theory of Nonlinear Programming -- A. Constrained Optimization -- B. Kuhn-Tucker Optimization -- III. Linearization of Nonlinear Programming Problems -- A. Linear Approximations and Linear Programming -- B. Partitioning of Variables -- C. Separable Programming -- IV. Quadratic Programming -- A. Linear and Quadratic Programming -- B. The Kuhn-Tucker Conditions -- C. Combinatorial Solution -- D. Wolfe’s Method -- E. The Simplex Method for Quadratic Programming -- F. Beale’s Method -- G. Computer Solution -- H. Some Industrial Applications -- V. Dynamic Programming and Multistage Optimization -- VI. Applications of Dynamic Programming -- A. The Shortest Path through a Network -- B. Production Planning -- C. Inventory Problems -- D. Investment Planning -- E. Allocation of Salesmen -- F. Cargo Loading and the Knapsack Problem -- VII. Several Decision and State Variables -- VIII. Infinite-Stage Problems -- IX. Dynamic Programming under Risk -- A. Risk and Multistage Optimization -- B. Dynamic Programming and Markov Processes -- X. Appendix: The Recursion Procedure in Dynamic Programming -- A. Stage Optimization -- B. Backward Recursion for Given Initial State -- C. Forward Recursion for Given Initial State -- D. Forward Recursion for Given Final State -- E. Backward Recursion for Given Final State -- F. Given Initial and Final States -- Answers to Exercises -- References.