3341.454: Mathematical and Numerical Optimization

3341.454: Mathematical and Numerical Optimization, Spring 2026

Instructor: Dabeen Lee (27-205)
Email: dabeenl [at] snu [dot] ac [dot] kr

This course provides a comprehensive introduction to mathematical and numerical optimization, covering both theory (convex analysis, linear and conic programming, optimality conditions, duality) and algorithms (the simplex method, gradient descent and its variants, proximal and splitting methods, Newton and quasi-Newton methods, interior point methods) as well as an introduction to integer programming.

Lecture notes

  1. Wed 3/04: course introduction, convex sets, convex functions, first- and second-order characterizations of convex functions (note)
  2. Mon 3/09: operations preserving convexity, convex optimization problems and applications (note)
  3. Wed 3/11: convex programming hierarchy, linear programming, optimization problems represented as linear programs (note)
  4. Mon 3/16: history of linear programming, standard form, simplex method, geometry of the simplex algorithm (note)
  5. Wed 3/18: two-phase simplex algorithm, infeasible and unbounded linear programs (note)
  6. Mon 3/23: quadratic programming, semidefinite programming, conic programming, second-order cone programming (note)
  7. Wed 3/25: conic duality theorem, optimality conditions for convex minimization (note)
  8. Mon 3/30: introduction to gradient descent, convergence of gradient descent (note)
  9. Wed 4/01: smooth functions, convergence of gradient descent for smooth functions (note)
  10. Mon 4/06: strongly convex functions, gradient descent for strongly convex functions, projected gradient descent (note)
  11. Wed 4/08: lower bounds on the iteration complexity of gradient methods, accelerated gradient method, projection-free method (note)
  12. Mon 4/13: proximal gradient descent and its convergence (note)
  13. Wed 4/15: LASSO, Nesterov's acceleration and FISTA, proximal point algorithm (note)
  14. Mon 4/20: smooth approximation, Fenchel conjugate (note)
  15. Mon 4/27: Moreau-Yosida smoothing, Lagrangian duality (note)
  16. Wed 4/29: Karush-Kuhn-Tucker conditions, saddle point problem, Lagrangian duality based on the Fenchel conjugate (note)
  17. Mon 5/04: dual gradient method for separable problems, augmented Lagrangian method, dual of composite minimization (note)
  18. Wed 5/06: optimization with functional constraints (note)
  19. Mon 5/11: fixed-point iteration (note)
  20. Wed 5/13: monotone operators, resolvents, operator splitting, Douglas-Rachford splitting and ADMM (note)
  21. Mon 5/18: Newton's method and its convergence (note)
  22. Wed 5/20: quasi-Newton methods (note)
  23. Mon 5/25: Newton's method for equality constrained minimization, barrier method (note)
  24. Wed 5/27: infeasible start Newton method, primal-dual interior point method (note)
  25. Mon 6/08: introduction to integer programming, integer programming formulations, convex hulls (note)
  26. Wed 6/10: methods for solving integer programs, Chvátal-Gomory cuts (note)

Assignments

  1. Assignment 1, due 4/08 (pdf)
  2. Assignment 2, due 5/25 (pdf)
  3. Assignment 3: paper review project, due 6/17 (pdf)