Optimization Theory

  1. Nonlinear Programming
    1. Equality Constrained Optimization
      1. Reduced Gradient Methods
        1. Variable Elimination
          1. Null Space Methods
          2. Sequential Quadratic Programming (SQP)
            1. QP Subproblem Formulation
              1. Hessian Approximation
                1. Merit Functions
                  1. Line Search in SQP
                  2. Augmented Lagrangian Methods
                    1. Penalty Parameter Updates
                      1. Multiplier Updates
                        1. Convergence Properties
                      2. Inequality Constrained Optimization
                        1. Active Set Methods
                          1. Working Set Strategy
                            1. Adding and Dropping Constraints
                              1. QP Subproblems
                              2. Interior Point Methods
                                1. Barrier Function Approach
                                  1. Primal-Dual Methods
                                    1. Central Path Following
                                    2. Sequential Linear Programming (SLP)
                                      1. Sequential Quadratic Programming Extensions
                                      2. Penalty and Barrier Methods
                                        1. Exterior Penalty Methods
                                          1. Quadratic Penalty Functions
                                            1. Exact Penalty Functions
                                            2. Interior Penalty Methods
                                              1. Logarithmic Barriers
                                                1. Inverse Barriers
                                                2. Augmented Lagrangian Methods
                                                  1. Method of Multipliers
                                                    1. ADMM (Alternating Direction Method of Multipliers)
                                                  2. Global Optimization Techniques
                                                    1. Branch and Bound for Nonlinear Problems
                                                      1. Cutting Plane Methods
                                                        1. Lipschitz Optimization
                                                          1. Interval Analysis Methods

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                                                        5. Linear Programming

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                                                        7. Integer and Combinatorial Optimization