Theory of Optimization

This course introduces the fundamentals of optimization, focusing on finding minima or maxima of objective functions, possibly under constraints. Students learn the basic definitions, and explore first and second order necessary and sufficient conditions to identify and classify stationary points (including local minima, maxima, and saddle points). The course covers basics of convex analysis, emphasizing why convexity guarantees a local minimum is global, and introduces the gradient method for practical optimization. The material is suitable for anyone interested in the mathematical foundations and algorithmic approaches in optimization theory.

Co-taught in Summer 2024 and Summer 2025 at Ho Chi Minh City University of Education.