Innovations in the use of Second Derivatives in Large-Scale Sparse Optimization
Abstract
The project will continue the development of highly e~cient and innovative algorithms for solving large-scale sparse constrained non"linear optimization problems. The polyhedral active set algorithm (PASA), developed in an ongoing ONR project, utilizes function val"ues and gradients to achieve fast and robust convergence and accurate solutions in a broad class of problems. The goal in the new on"e year project is to enhance PASA through the use of second derivative information, when it is available. This will enable rapid con"vergence in some large and ill conditioned conditioned optimization problems where gradient-based algorithms can be slow.The appro"ach to be developed amounts to replacing the objective function in phase two of PASA, where a linearly constrained optimization prob""lem is solved, by a second-order Taylor expansion modi~ed by a small penalty term. The penalty term leads to a positive semide~nite"" Hessian in a neighborhood of an optimum, making the problem amenable to conjugate gradient iterative techniques or a direct Cholesk"y factorization.The optimization algorithm is a key component in the new platform for optimal control being developed in the ongoi"ng work. As the optimization algorithm becomes faster and more robust, the new optimal control platform becomes more reliable and be""tter suited for real-time control. The research will bene~t actual applications of interest to the U.S. Navy, such as the optimizati""on of a UAV, as well as other applications of national importance.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jan 23, 2018
- Source ID
- N000141812100
Entities
People
- William Hager
Organizations
- Office of Naval Research
- United States Navy
- University of Florida