Abstract. Optimization is an endlessly fascinating field that comes in many flavors, shapes, and sizes. It ranges from research that is entirely theoretical, without apparent connection to any application, to the nitty-gritty implementation of computational methods for solving real-world problems. It not only covers everything in between, but also has deep interconnections with other areas such as linear algebra, differential equations, and approximation.
Certain mathematical techniques are widely used in characterizing optimality, developing optimization methods, and proving their convergence in both exact and finite precision. In addition, there are numerous instances in which the needed mathematics comes from far afield. This talk will give an overview, necessarily selective, of the mathematics associated with modern continuous optimization.