CSE426 Optimization Methods

Instructor:Assoc. Prof. Dr. Yuriy Mishchenko (Toros University)



An introduction to the modern theory and methods of numerical optimization for computer/software engineering and computer science students.


  1. Introduction to the subject of numerical optimization
  2. General optimization problem, extremality conditions, extrema of a quadratic form
  3. Newton-Raphson optimization method
  4. Gradient descend optimization
  5. Trust regions, quasi Newton methods, DFP and BFGS; line search methods, backtracking, Armijo rule, Wolfe conditions
  6. Levenberg-Marquardt method
  7. Constrained optimization, general equality constraints, the method of Lagrange multipliers
  9. General inequality constraints, KKT theory, KKT equations, dual problems
  10. The methods of nonlinear constrained optimization, barrier method, interior point method
  11. Karmarkar's algorithm and its significance
  12. The theory of convex optimization, convex functions and their properties
  13. Constrained convex optimization, the art of constructing convex optimization programs
  14. Overview of main types of convex optimization programs; linear programming, quadratic programming, cone programming, SOCP, geometric programming, semidefinite programming


Evaluation is performed according to the corresponding Faculty guidelines.

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