Introduction to Optimization

This lecture introduces the fundamentals of optimization, covering linear, discrete, and nonlinear optimization. It includes historical perspectives, mathematical formulations, and practical applications. Topics range from the simplex method to Lagrangian methods and approximation algorithms. The instructor emphasizes the importance of decision variables, objective functions, and constraints in building optimization models. Practical examples such as the Diet Problem, Manufacturing Problem, and Investment Problem are discussed to illustrate real-world applications of optimization techniques.