NDLI: An operator theoretic framework for analysis of large-scale quadratic programming

Content Provider	IEEE Xplore Digital Library
Author	Motee, N. Jadbabaie, A.
Copyright Year	2007
Description	Author affiliation: Univ. of Pennsylvania, Philadelphia (Motee, N.; Jadbabaie, A.)
Abstract	One of the fundamental problems in the area of large-scale constrained optimization problems is the study of the locality features of spatially distributed optimization problems, which can motivate the development of fast and well-conditioned distributed algorithms. We study the spatial locality features of large-scale, possibly infinite-dimensional, quadratic programming (QP) problems with linear inequality constraints. Examples of such problems include receding horizon control of spatially distributed linear systems with input and state constraints, optimal estimation of a parameter based on data collected in a sensor network, manifold learning of a large set of data in machine learning, etc. We propose a new approach for analysis of large-scale QP problems by blending tools from duality theory with operator theory. The class of spatially decaying matrices is introduced to capture couplings between optimization variables in the cost function and constraints. We show that the optimal solution of a large-scale convex QP is piece-wise affine- represented as convolution sums. More importantly, we prove that the kernel of each convolution sum decays in the spatial domain at a rate proportional to the inverse of the corresponding coupling function of the optimization problem. Simulations results are provided to verify our theoretical results.
Starting Page	830
Ending Page	835
File Size	333452
Page Count	6
File Format	PDF
ISBN	9781424414970
ISSN	01912216
DOI	10.1109/CDC.2007.4434725
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2007-12-12
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Large-scale systems Quadratic programming Constraint optimization Machine learning Convolution Distributed algorithms Optimal control Distributed control Control systems Linear systems
Content Type	Text
Resource Type	Article

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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