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- W2801974316 abstract "We study the following optimization problem over a dynamical system that consists of several linear subsystems: Given a finite set of $ntimes n$ matrices and an $n$-dimensional vector, find a sequence of $K$ matrices, each chosen from the given set of matrices, to maximize a convex function over the product of the $K$ matrices and the given vector. This simple problem has many applications in operations research and control, yet a moderate-sized instance is challenging to solve to optimality for state-of-the-art optimization software. We propose a simple exact algorithm for this problem. Our algorithm runs in polynomial time when the given set of matrices has the oligo-vertex property, a concept we introduce in this paper for a finite set of matrices. We derive several sufficient conditions for a set of matrices to have the oligo-vertex property. Numerical results demonstrate the clear advantage of our algorithm in solving large-sized instances of the problem over one state-of-the-art global optimization solver. We also propose several open questions on the oligo-vertex property and discuss its potential connection with the finiteness property of a set of matrices, which may be of independent interest." @default.
- W2801974316 created "2018-05-17" @default.
- W2801974316 creator A5013185546 @default.
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- W2801974316 date "2018-05-12" @default.
- W2801974316 modified "2023-09-27" @default.
- W2801974316 title "Optimal switching sequence for switched linear systems" @default.
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- W2801974316 doi "https://doi.org/10.48550/arxiv.1805.04677" @default.
- W2801974316 hasPublicationYear "2018" @default.
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