Optimization Theory

  1. Dynamic Programming
    1. Theoretical Foundations
      1. Principle of Optimality
        1. Bellman's Equation
          1. Value Functions
            1. Policy Functions
            2. Deterministic Dynamic Programming
              1. Finite Horizon Problems
                1. Backward Induction
                  1. Forward Recursion
                  2. Infinite Horizon Problems
                    1. Discounted Problems
                      1. Undiscounted Problems
                      2. Continuous State and Control
                      3. Stochastic Dynamic Programming
                        1. Markov Decision Processes
                          1. States, Actions, and Transitions
                            1. Reward Functions
                              1. Policies and Value Functions
                              2. Value Iteration
                                1. Policy Iteration
                                  1. Linear Programming Formulation
                                  2. Applications and Extensions
                                    1. Shortest Path Problems
                                      1. Resource Allocation Over Time
                                        1. Inventory Control Models
                                          1. Optimal Stopping Problems
                                            1. Stochastic Control Problems
                                            2. Computational Aspects
                                              1. Curse of Dimensionality
                                                1. Approximation Methods
                                                  1. Function Approximation
                                                    1. Approximate Dynamic Programming

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                                                  7. Integer and Combinatorial Optimization

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                                                  9. Stochastic Optimization