Operations Research and Optimization

  1. Advanced Optimization Topics
    1. Large-Scale Optimization
      1. Computational Challenges
        1. Memory Requirements
          1. Computational Time
            1. Numerical Stability
            2. Decomposition Methods
              1. Problem Structure Exploitation
                1. Subproblem Coordination
                2. Dantzig-Wolfe Decomposition
                  1. Master Problem
                    1. Subproblems
                      1. Column Generation
                        1. Pricing Problems
                        2. Benders Decomposition
                          1. Primal Decomposition
                            1. Dual Cuts
                              1. Mixed-Integer Applications
                                1. L-Shaped Method
                                2. Lagrangian Decomposition
                                  1. Dual Problem
                                    1. Subgradient Methods
                                      1. Coordination Mechanisms
                                    2. Stochastic Programming
                                      1. Uncertainty Modeling
                                        1. Random Parameters
                                          1. Probability Distributions
                                            1. Scenario Trees
                                            2. Two-Stage Stochastic Programming
                                              1. First-Stage Decisions
                                                1. Second-Stage Decisions
                                                  1. Recourse Actions
                                                    1. Expected Value Problems
                                                    2. Multi-Stage Stochastic Programming
                                                      1. Sequential Decision Making
                                                        1. Information Revelation
                                                          1. Non-Anticipativity Constraints
                                                          2. Solution Methods
                                                            1. Sample Average Approximation
                                                              1. Progressive Hedging
                                                                1. Scenario Decomposition
                                                                2. Scenario Generation
                                                                  1. Monte Carlo Sampling
                                                                    1. Moment Matching
                                                                      1. Scenario Reduction
                                                                        1. Scenario Tree Construction
                                                                      2. Robust Optimization
                                                                        1. Uncertainty Sets
                                                                          1. Box Uncertainty
                                                                            1. Ellipsoidal Uncertainty
                                                                              1. Polyhedral Uncertainty
                                                                              2. Robust Counterparts
                                                                                1. Worst-Case Optimization
                                                                                  1. Robust Feasibility
                                                                                    1. Robust Optimality
                                                                                    2. Adjustable Robust Optimization
                                                                                      1. Wait-and-See Decisions
                                                                                        1. Here-and-Now Decisions
                                                                                          1. Affine Decision Rules
                                                                                          2. Applications
                                                                                            1. Portfolio Optimization
                                                                                              1. Supply Chain Management
                                                                                                1. Network Design
                                                                                              2. Multi-Objective Optimization
                                                                                                1. Problem Formulation
                                                                                                  1. Multiple Criteria
                                                                                                    1. Conflicting Objectives
                                                                                                      1. Trade-off Analysis
                                                                                                      2. Pareto Optimality
                                                                                                        1. Efficient Solutions
                                                                                                          1. Pareto Front
                                                                                                            1. Weak Pareto Optimality
                                                                                                            2. Scalarization Methods
                                                                                                              1. Weighted Sum Method
                                                                                                                1. Epsilon-Constraint Method
                                                                                                                  1. Achievement Scalarizing Functions
                                                                                                                  2. Goal Programming
                                                                                                                    1. Goal Constraints
                                                                                                                      1. Deviation Variables
                                                                                                                        1. Priority Levels
                                                                                                                          1. Lexicographic Goal Programming
                                                                                                                          2. Interactive Methods
                                                                                                                            1. Progressive Articulation
                                                                                                                              1. Reference Point Methods
                                                                                                                                1. Trade-off Information
                                                                                                                                2. Evolutionary Multi-Objective Optimization
                                                                                                                                  1. Population-Based Approaches
                                                                                                                                    1. Pareto Ranking
                                                                                                                                      1. Diversity Preservation
                                                                                                                                    2. Combinatorial Optimization
                                                                                                                                      1. Graph-Based Problems
                                                                                                                                        1. Traveling Salesman Problem
                                                                                                                                          1. Vehicle Routing Problem
                                                                                                                                            1. Graph Coloring
                                                                                                                                              1. Maximum Clique
                                                                                                                                              2. Scheduling Problems
                                                                                                                                                1. Job Shop Scheduling
                                                                                                                                                  1. Flow Shop Scheduling
                                                                                                                                                    1. Parallel Machine Scheduling
                                                                                                                                                    2. Packing and Cutting Problems
                                                                                                                                                      1. Bin Packing
                                                                                                                                                        1. Cutting Stock
                                                                                                                                                          1. Knapsack Variants
                                                                                                                                                          2. Location Problems
                                                                                                                                                            1. Facility Location
                                                                                                                                                              1. Hub Location
                                                                                                                                                                1. Covering Problems
                                                                                                                                                              2. Convex Optimization
                                                                                                                                                                1. Convex Problem Classes
                                                                                                                                                                  1. Linear Programming
                                                                                                                                                                    1. Quadratic Programming
                                                                                                                                                                      1. Second-Order Cone Programming
                                                                                                                                                                        1. Semidefinite Programming
                                                                                                                                                                        2. Duality in Convex Optimization
                                                                                                                                                                          1. Lagrangian Duality
                                                                                                                                                                            1. Strong Duality
                                                                                                                                                                              1. KKT Conditions
                                                                                                                                                                              2. Interior Point Methods
                                                                                                                                                                                1. Barrier Methods
                                                                                                                                                                                  1. Path-Following Methods
                                                                                                                                                                                    1. Predictor-Corrector Methods
                                                                                                                                                                                    2. First-Order Methods
                                                                                                                                                                                      1. Gradient Methods
                                                                                                                                                                                        1. Proximal Methods
                                                                                                                                                                                          1. Accelerated Methods

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                                                                                                                                                                                      11. Heuristics and Metaheuristics

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                                                                                                                                                                                      1. Introduction to Operations Research