Innovations in Large-Scale Sparse Optimization and Applications
Abstract
Innovations in Large-Scale Sparse Optimization and Applications The project will develop highly e cient and innovative algorithms for solving large-scale sparse constrained nonlinear optimization problems. A new nonsmooth approach will iden- tify inactive constraints quickly and remove them from the problem, while a new algorithm will be developed for fast projection onto a polyhedron. The fast projection algorithm exploits the existing sparsity by only operating on the nonzeros in the constraints, and it enhances sparsity when linear equations are solved by reordering the equations to reduce ll-in during a Cholesky factorization. The projection algorithm will be incorporated into a new active set strategy for polyhedral constrained nonlinear optimization. The polyhedral projection algorithm and the active set algorithm, along with a recent new approach for error and multiplier estimation in nonlinear optimization will be used in a iterative fashion to obtain accurate solutions of general nonlinear optimization problems. In addition, a new operator overloading approach will be developed for algorithmically evaluating derivatives used by the new NLP solver. With the new approach, the user could describe his functions in a high level language like MATLAB that supports operator overloading, and then directly generate the derivatives in either the high level language or in a compiled language such as C or Fortran. The algorithmic di erentiator will also yield the nonlinear sparsity of the optimization problem, which will increase the e ciency of the NLP solver. As the optimization software is developed, it will be tested using a new platform for optimal control called GPOPS ?? II (General Pseudospectral Optimal Control Software), which comes equipped with a library of test problems arising in practical applications. Since discretized optimal control problems reduce to large, highly constrained sparse non- linear programming problems, this will be an ideal test bed for the new optimization al- gorithms. Since GPOPS ?? II has a large user base that encompasses the Department of Defense, universities, and industry, the research will have immediate broad impact. The numerical experiments with GPOPS ?? II should improve the robustness of the optimiza- tion algorithms, while the accurate NLP solver will enable further development of the mesh re nement algorithms. The proposed research should bene t any application that leads to a large sparse nonlinear optimization problem that needs to be solved quickly with high accuracy.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 12, 2016
- Source ID
- N000141512048
Entities
People
- William Ward Hager
Organizations
- Office of Naval Research
- United States Navy
- University of Florida