This course provides a comprehensive study of optimization theory and computational methods, from classical linear programming to modern data science applications. Students will learn to formulate real-world problems as mathematical optimization models and solve them using appropriate algorithms — covering exact methods, heuristics, and state-of-the-art techniques used in industry and research.
What You Will Learn
- Mathematical Foundations — Convexity, gradients, Hessians, and optimality conditions
- Linear & Integer Programming — Simplex method, duality, sensitivity analysis, branch-and-bound
- Network Optimization — Shortest path, maximum flow, minimum spanning tree algorithms
- Nonlinear Optimization — Gradient descent, Newton's method, KKT conditions
- Dynamic Programming & Metaheuristics — DP formulations, simulated annealing, genetic algorithms
- Stochastic & Robust Optimization — Decision-making under uncertainty, Monte Carlo simulation
- Game Theory — Nash equilibrium, mechanism design, and optimization in strategic settings
- Modern Applications — Machine learning optimization, big data, combinatorial optimization
- Giáo viên: Nguyễn Minh Hải