Professor Nocedal research interests are in optimization and its application in machine learning and in disciplines involving differential equations. He specializes in nonlinear optimization, both convex and non-convex; deterministic and stochastic. There is a need for solving ever larger optimization problems, and throughout the years, he has developed algorithms that scale well with the number of variables, make judicious use of second-order information, and parallelize well. The motivation for his current algorithmic and theoretical research stems from applications in image and speech recognition, recommendation systems, and search engines.