Nonlinear Optimization

This graduate course offers a unified analytical and computational approach to nonlinear optimization problems. Unconstrained optimization methods include gradient, conjugate direction, Newton, sub-gradient, and first-order methods. Constrained optimization methods include feasible directions, projection, interior point methods, and Lagrange multiplier methods. The curriculum covers convex analysis, Lagrangian relaxation, and nondifferentiable optimization, as well as applications in integer programming. It provides a comprehensive treatment of optimality conditions and Lagrange multipliers, and uses a geometric approach to duality theory. Applications are drawn from control, communications, machine learning, and resource allocation problems.