Research Summaries

Back Development of An Optimal Control Theory for Nonlinear and Accelerated Optimization

Fiscal Year 2019
Division Graduate School of Engineering & Applied Science
Department Mechanical & Aerospace Engineering
Investigator(s) Ross, Isaac M.
Sponsor Air Force Office of Scientific Research (Air Force)
Summary This proposal is to develop a new theory for nonlinear optimization including accelerated optimization. The proposed theory is based on a revolutionary new idea of using optimal control concepts for nonlinear programming (NLP). It is revolutionary in the sense that while it is customary to use NLP techniques for optimal control, the idea of doing the inverse is quite radical. This is precisely what we aim to do in this proposal. The directional derivatives of the objective- and constraint-functions supply the vector fields for the optimal control problem with the search vector as the control variable. A new direction of research in NLP theory and computation is now possible. For instance, we can show that zero-Hamiltonian singular extremals of the optimal control problem constitute the ``optimal'' search path for the NLP. A thorough exploration of these ideas is proposed.
Keywords Deep Learning accelerated optimization heavy-ball method optimal control theory transversality mapping principle
Publications Publications, theses (not shown) and data repositories will be added to the portal record when information is available in FAIRS and brought back to the portal
Data Publications, theses (not shown) and data repositories will be added to the portal record when information is available in FAIRS and brought back to the portal