Optimization Theory

  1. Integer and Combinatorial Optimization
    1. Problem Formulations
      1. Pure Integer Programming
        1. Mixed-Integer Linear Programming (MILP)
          1. Mixed-Integer Nonlinear Programming (MINLP)
            1. Binary Integer Programming
              1. Combinatorial Optimization Problems
              2. Solution Methodologies
                1. Enumeration Methods
                  1. Complete Enumeration
                    1. Branch and Bound
                      1. Branching Strategies
                        1. Bounding Techniques
                          1. Node Selection Rules
                            1. Pruning Conditions
                          2. Cutting Plane Methods
                            1. Gomory Cuts
                              1. Chvátal-Gomory Cuts
                                1. Lift-and-Project Cuts
                                  1. Disjunctive Cuts
                                  2. Branch and Cut
                                    1. Integration of Branching and Cutting
                                      1. Cut Generation Strategies
                                        1. Preprocessing Techniques
                                      2. Specialized Integer Programming Topics
                                        1. Knapsack Problems
                                          1. 0-1 Knapsack Problem
                                            1. Unbounded Knapsack Problem
                                              1. Multiple Knapsack Problems
                                              2. Set Covering and Packing Problems
                                                1. Traveling Salesman Problem
                                                  1. Network Flow Problems with Integer Variables
                                                  2. Approximation Algorithms
                                                    1. Performance Guarantees
                                                      1. Greedy Algorithms
                                                        1. Local Search Approximations
                                                          1. Randomized Algorithms
                                                          2. Computational Complexity
                                                            1. NP-Completeness
                                                              1. Polynomial-Time Approximation Schemes
                                                                1. Fixed-Parameter Tractability

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                                                              6. Nonlinear Programming

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                                                              8. Dynamic Programming