Numerical Methods

  1. Optimization Methods
    1. Unconstrained Optimization
      1. Multidimensional Methods
        1. Gradient Descent
          1. Steepest Descent
            1. Step Size Selection
              1. Convergence Rate
              2. Newton's Method
                1. Hessian Matrix
                  1. Quadratic Convergence
                    1. Implementation Issues
                    2. Quasi-Newton Methods
                      1. BFGS Method
                        1. DFP Method
                          1. Secant Conditions
                          2. Conjugate Gradient
                            1. Fletcher-Reeves
                              1. Polak-Ribière
                                1. Linear Conjugacy
                              2. Line Search Methods
                                1. Wolfe Conditions
                                  1. Backtracking
                                2. Constrained Optimization
                                  1. Linear Programming
                                    1. Standard Form
                                      1. Simplex Method
                                        1. Basic Solutions
                                          1. Pivot Operations
                                            1. Optimality Conditions
                                            2. Duality Theory
                                            3. Nonlinear Constraints
                                              1. Lagrange Multipliers
                                                1. KKT Conditions
                                                  1. Penalty Methods
                                                    1. Barrier Methods
                                                      1. Sequential Quadratic Programming

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                                                  10. Partial Differential Equations

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                                                  12. Eigenvalue Problems