Optimization Theory

  1. Specialized Optimization Topics
    1. Convex Optimization
      1. Conic Programming
        1. Linear Programming as Conic
          1. Second-Order Cone Programming
            1. Semidefinite Programming
            2. Interior Point Methods for Convex Problems
              1. Proximal Methods
                1. Proximal Gradient Method
                  1. Accelerated Proximal Methods
                  2. Dual Methods
                    1. Dual Ascent
                      1. Dual Decomposition
                        1. ADMM Applications
                      2. Network Optimization
                        1. Shortest Path Problems
                          1. Dijkstra's Algorithm
                            1. Bellman-Ford Algorithm
                              1. Floyd-Warshall Algorithm
                              2. Maximum Flow Problems
                                1. Ford-Fulkerson Algorithm
                                  1. Push-Relabel Algorithms
                                  2. Minimum Cost Flow Problems
                                    1. Network Design Problems
                                    2. Game Theory and Optimization
                                      1. Nash Equilibrium
                                        1. Stackelberg Games
                                          1. Cooperative Game Theory
                                            1. Mechanism Design
                                            2. Variational Methods
                                              1. Calculus of Variations
                                                1. Optimal Control Theory
                                                  1. Pontryagin's Maximum Principle
                                                    1. Hamilton-Jacobi-Bellman Equation

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                                                  11. Multi-Objective Optimization

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                                                  13. Applications and Case Studies