Mathematical Optimization

1. Advanced Topics in Optimization
   1. Global Optimization
      1. Techniques for avoiding local minima
         1. Evolutionary algorithms
            1. Genetic algorithms and their variants
            2. Differential evolution
         2. Simulated annealing
         3. Basin-hopping methods
         4. Deterministic global optimization techniques
            1. Branch and bound for non-convex problems
            2. Interval analysis
      2. Multistart methods
      3. Hybrid approaches combining global and local search
   2. Bilevel and Multilevel Optimization
      1. Hierarchical problem solving
         1. Concepts of leader-follower dynamics
         2. Sequential decision making
      2. Bilevel optimization techniques
         1. KKT conditions for bilevel problems
         2. Evolutionary bilevel optimization
         3. Approximate bilevel methods
      3. Multilevel optimization
         1. Applications in energy systems and hierarchical resource allocation
         2. Nested optimization problems
   3. Machine Learning and Optimization
      1. Optimization in training algorithms
         1. Stochastic gradient descent and its variants
         2. Adaptive learning rate methods (e.g., Adam, RMSprop)
         3. Second-order optimization methods
      2. Hyperparameter optimization
         1. Grid search and random search
         2. Bayesian optimization
         3. Hyperband and successive halving
         4. Evolutionary and genetic approaches
      3. Optimization for deep learning
         1. Backpropagation and gradient-based learning
         2. Overfitting solutions and regularization techniques
   4. Quantum Optimization
      1. Quantum annealing
         1. D-Wave systems and applications
         2. Quantum annealing vs classical annealing
      2. Quantum-inspired algorithms
         1. Quantum-inspired evolutionary algorithms
         2. Quantum approximate optimization algorithm (QAOA)
      3. Applications in complex systems
         1. Cryptography and security
         2. Material science
         3. Drug discovery and healthcare optimization
   5. Other Emerging Topics
      1. Robust optimization
         1. Dealing with uncertainty and variability
         2. Applications in finance and supply chain
      2. Stochastic optimization
         1. Stochastic approximation and robust stochastic methods
         2. Applications under uncertainty
      3. Online and real-time optimization
         1. Algorithm adaptation in dynamic environments
         2. Real-time decision systems
      4. Multi-objective and Pareto optimization
         1. Advanced techniques for large-scale multi-objective problems
         2. Trade-off analysis and decision making with conflicting objectives