The goal of this course is to introduce the basic theoretical principles underlying nonlinear optimization and the numerical algorithms that are used to solve them.  We begin with fundamental (sub)gradient methods and Newton’s method for unconstrained optimization, which represent the basis of most nonlinear optimization algorithms.  We then develop an understanding of optimality conditions and duality in the presence of nonlinear functions, ending by discussing modern numerical methods for nonlinear constrained optimization, and their associated convergence properties.  Group projects are a major aspect of this course, which serve as a way of learning through implementation and  experimentation.