For decades, a great deal of nonlinear optimization research has focused on modeling and solving convex problems. This has been due to the fact that convex objects typically represent satisfactory estimates of real-world phenomenon, and since convex objects have very nice mathematical properties that makes analyses of them relatively straightforward. However, this focus has been changing. In various important applications, such as large-scale data fitting and learning problems, researchers are starting to turn away from simple, convex models toward more challenging nonconvex models that better represent real-world behaviors and can offer more useful solutions.
To contribute to this new focus on nonconvex optimization models, I defined my research to present new techniques for solving nonconvex optimization problems that possess attractive theoretical and practical properties.

 

Publications

• F. E. Curtis, D. P. Robinson, and M. Samadi. A Trust Region Algorithm with a Worst-Case Iteration Complexity of O(ε^(-3/2)) for Nonconvex Optimization. Mathematical Programming, 162(1), 1-32, 2017, DOI 10.1007/s10107-016-1026-2.
• F. E. Curtis, D. P. Robinson, and M. Samadi. Complexity Analysis of a Trust Funnel Algorithm for Equality Constrained Optimization. Accepted for publication in the SIAM Journal on Optimization.
• F. E. Curtis, D. P. Robinson, and M. Samadi. An Inexact Regularized Newton Framework with a Worst-Case Iteration Complexity of O(ε^(-3/2)) for Nonconvex Optimization. Accepted for publication in the IMA Journal of Numerical Analysis.

Invited Conference Talks

• A Trust-Funnel Algorithm for Nonconvex Equality Constrained Optimization with O(ε^(-3/2)) Complexity, U.S. and Mexico Workshop on Optimization and its Applications, Huatulco, Mexico, January 2018.
• A Trust-Funnel Algorithm for Nonconvex Equality Constrained Optimization with O(ε^(-3/2)) Complexity, INFORMS Annual Meeting, Houston, TX, USA, October 2017.
• Efficient Trust-Region Methods for Nonconvex Optimization, INFORMS Annual Meeting, Nashville, TN, USA, November 2016.
• Efficient Trust-Region Methods for Nonconvex Optimization, ICCOPT Conference, Tokyo, Japan, August 2016.
• A Trust-Region Algorithm with a Worst-Case Iteration Complexity of O(ε^(-3/2)) for Nonconvex Optimization, INFORMS Annual Meeting, Philadelphia, PA, USA, November 2015.
• A Trust-Region Algorithm with Improved Complexity for Nonconvex Optimization, MOPTA Conference, Bethlehem, PA, USA, July 2015.