Learning Outcomes
The purpose of the course is for the course participant to develop basic knowledge and skills in optimization methods.
On the completion of the course, the student will be able to:
1. Construct optimization problems;
2. Determine if an optimization problem can be solved;
3. Construct and analyze optimization algorithms for nonlinear problems, with or without constraints.
Course Content (Syllabus)
Basic principles (convex sets and functions, optimality conditions, duality);
Unconstrained optimization (line search with and without using derivatives, gradient methods, the Levenberg-Marquardt modification, quasi-newton and conjugate gradient methods);
Constrained optimization (penalty function methods, barrier function methods, methods of feasible directions, augmented Lagrangian methods);
Convergence and speed of convergence analysis;
Global optimization (simulated annealing, evolutionary algorithms).