Mathematical Optimization

1. Applications of Mathematical Optimization
   1. Engineering Design
      1. Structural Optimization
         1. Shape optimization
         2. Topology optimization
         3. Sensitivity analysis in structural design
         4. Case studies in aeronautical and civil engineering
      2. Control Systems
         1. Optimal control theory
         2. Model predictive control
         3. System identification and optimization
         4. Real-time control systems optimization
   2. Economics and Finance
      1. Portfolio Optimization
         1. Mean-variance optimization
         2. Risk-return trade-offs
         3. Asset allocation strategies
         4. Incorporating transaction costs and taxes
      2. Risk Management
         1. Optimization in credit risk assessment
         2. Stress testing and scenario analysis
         3. Value-at-risk (VaR) models
         4. Optimizing insurance strategies
   3. Supply Chain and Logistics
      1. Inventory Management
         1. Economic order quantity (EOQ) models
         2. Just-in-time (JIT) optimization
         3. Multi-echelon inventory optimization
         4. Demand forecasting and optimization
      2. Vehicle Routing
         1. Capacitated vehicle routing problem (CVRP)
         2. Time window constraints in vehicle routing
         3. Heuristics and exact methods for routing
         4. Integration of routing with real-time traffic data
   4. Operations Research
      1. Resource Allocation
         1. Linear programming in resource allocation
         2. Multi-period allocation models
         3. Workforce optimization
         4. Energy resource management
      2. Scheduling and Planning
         1. Job-shop scheduling problems
         2. Project scheduling and critical path methods
         3. Optimization in manufacturing processes
         4. Dynamic scheduling in uncertain environments
      3. Network Optimization
         1. Flow optimization in networks
         2. Reliability and scalability in network planning
         3. Telecommunications network design
         4. Transportation network optimization