Upon completion of the course, the students will be able to:
a) design and analyze optimization problems;
b) design and analyze optimization algorithms for nonlinear problems, with or without constraints;
c) implement optimization algorithms in MATLAB.
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).
Additional bibliography for study
1. D.P. Bertsekas, Nonlinear Programming, Athena Scientific, Belmont, Massachusetts, 1999.
2. M.S. Bazaraa, H.D. Sherali, C.M. Shetty, Nonlinear Programming Theory and Algorithms, John Wiley and Sons, New York, 1993.