期刊
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
卷 63, 期 7, 页码 2131-2138出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2017.2754474
关键词
Kalman smoothing; Nonconvex optimization; PDE constrained optimization; variable projection
资金
- Washington Research Foundation Data Science Professorship
- AFOSR YIP [FA9550-15-1-0237]
- Netherlands Organisation of Scientific Research [613.009.032]
Common computational problems, such as parameter estimation in dynamic models and partial differential equation (PDE)-constrained optimization, require data fitting over a set of auxiliary parameters subject to physical constraints over an underlying state. Naive quadratically penalized formulations, commonly used in practice, suffer from inherent ill-conditioning. We show that surprisingly the partial minimization technique regularizes the problem, making it well-conditioned. This viewpoint sheds newlight on variable projection techniques, as well as the penalty method for PDE-constrained optimization, and motivates robust extensions. In addition, we outline an inexact analysis, showing that the partial minimization subproblem can be solved very loosely in each iteration. We illustrate the theory and algorithms on boundary control, optimal transport, and parameter estimation for robust dynamic inference.
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