Many challenges in contemporary computational mathematics can be expressed as optimization of an objective subject to appropriate constraints. Oscar Bruno develops techniques for engineering design in aeronautics, fluid-mechanics, and photonics applications. Venkat Chandrasekaran uses optimization tools to introduce new methodologies in signal processing, statistical inference, and approximation theory. Joel Tropp has designed algorithms for sparse optimization, linear algebra computations, and semidefinite programming. Houman Owhadi has introduced Optimal Uncertainty Quantification and techniques for computing with non-finite information and optimization methods for discovering mathematical (Selberg) identities. Adam Wierman focuses on optimization in online settings, with applications to control and networked systems. Tom Hou has used manifold optimization tools to study low rank matrix recovery problems and proved a nearly optimal rate of convergence of Riemannian gradient descent for matrix sensing, phase retrieval and low rank matrix recovery.
Optimization is also a primary language for machine learning and for automatic control.
