98,575 research outputs found
Conic Optimization Theory: Convexification Techniques and Numerical Algorithms
Optimization is at the core of control theory and appears in several areas of
this field, such as optimal control, distributed control, system
identification, robust control, state estimation, model predictive control and
dynamic programming. The recent advances in various topics of modern
optimization have also been revamping the area of machine learning. Motivated
by the crucial role of optimization theory in the design, analysis, control and
operation of real-world systems, this tutorial paper offers a detailed overview
of some major advances in this area, namely conic optimization and its emerging
applications. First, we discuss the importance of conic optimization in
different areas. Then, we explain seminal results on the design of hierarchies
of convex relaxations for a wide range of nonconvex problems. Finally, we study
different numerical algorithms for large-scale conic optimization problems.Comment: 18 page
An essentially decentralized interior point method for control
Distributed and decentralized optimization are key for the control of
networked systems. Application examples include distributed model predictive
control and distributed sensing or estimation. Non-linear systems, however,
lead to problems with non-convex constraints for which classical decentralized
optimization algorithms lack convergence guarantees. Moreover, classical
decentralized algorithms usually exhibit only linear convergence. This paper
presents an essentially decentralized primal-dual interior point method with
convergence guarantees for non-convex problems at a {super}linear rate. We show
that the proposed method works reliably on a numerical example from power
systems. Our results indicate that the proposed method outperforms ADMM in
terms of computation time and computational complexity of the subproblems
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