A unified analytical and computational approach to nonlinear optimization problems. Unconstrained optimization methods include gradient, conjugate direction, Newton, and quasi-Newton methods. Constrained optimization methods include feasible directions, projection, interior point, and Lagrange multiplier methods. Convex analysis, Lagrangian relaxation, nondifferentiable optimization, and applications in integer programming. Comprehensive treatment of optimality conditions, Lagrange multiplier theory, and duality theory. Applications drawn from control, communications, power systems, and resource allocation problems. This is a course in the department's "Communication, Control, and Signal Processing" concentration. This course provides a unified analytical and computational approach to nonlinear optimization problems. The topics covered in this course include: unconstrained optimization methods, constrained optimization methods, convex analysis, Lagrangian relaxation, nondifferentiable optimization, and applications in integer programming. There is also a comprehensive treatment of optimality conditions, Lagrange multiplier theory, and duality theory. Throughout the course, applications are drawn from control, communications, power systems, and resource allocation problems. The materials are largely based on the textbook, Nonlinear Programming: 2nd Edition, written by Professor Dimitri Bertsekas (see http://www.athenasc.com/nonlinbook.html for more information).
