Optimization Methods (最优化方法)

MATH6015, Fall 2026 graduate public course

Course information

  • Course code: MATH6015
  • Term: Fall 2026
  • Level: Graduate public course (研究生公共课)
  • Instructor: Jingwei Liang

Course description

This course introduces the mathematical foundations, models, and algorithms of convex optimization. Topics include convex sets and functions, convex optimization problems, approximation and fitting, unconstrained and equality-constrained minimization, interior-point methods, statistical estimation, geometric problems, and selected first-order optimization methods.

Lecture notes

  1. Mathematical foundations
  2. Convexity and convex optimization
  3. Approximation and fitting
  4. Unconstrained minimization
  5. Equality-constrained minimization
  6. Interior-point methods
  7. Statistical estimation
  8. Geometric problems
  9. Supplement: first-order optimization methods

Reference

  • Stephen Boyd and Lieven Vandenberghe. Convex Optimization. Cambridge University Press, 2004. Book website.