Optimization Theory

  1. Stochastic Optimization
    1. Stochastic Programming Fundamentals
      1. Uncertainty Modeling
        1. Probability Distributions
          1. Scenario-Based Approaches
            1. Expected Value Problems
            2. Two-Stage Stochastic Programming
              1. Here-and-Now vs Wait-and-See Decisions
                1. Recourse Functions
                  1. L-Shaped Method
                    1. Benders Decomposition
                    2. Multi-Stage Stochastic Programming
                      1. Decision Trees
                        1. Scenario Trees
                          1. Non-Anticipativity Constraints
                            1. Progressive Hedging Algorithm
                            2. Chance-Constrained Programming
                              1. Individual Chance Constraints
                                1. Joint Chance Constraints
                                  1. Probabilistic Programming
                                    1. Sample Average Approximation
                                    2. Robust Optimization
                                      1. Uncertainty Sets
                                        1. Box Uncertainty
                                          1. Ellipsoidal Uncertainty
                                            1. Polyhedral Uncertainty
                                            2. Robust Counterpart Formulation
                                              1. Adjustable Robust Optimization
                                                1. Distributionally Robust Optimization
                                                2. Stochastic Approximation
                                                  1. Robbins-Monro Algorithm
                                                    1. Stochastic Gradient Methods
                                                      1. Convergence Analysis
                                                        1. Applications to Machine Learning

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                                                      8. Dynamic Programming

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                                                      10. Heuristic and Metaheuristic Methods