NDLI: Study of nonlinear power optimization problems using algebraic graph theory

Content Provider	IEEE Xplore Digital Library
Author	Sojoudi, S. Lavaei, J.
Copyright Year	2013
Description	Author affiliation: Dept. of Electr. Eng., Columbia Univ., New York, NY, USA (Lavaei, J.) \|\| Dept. of Comput. & Math. Sci., California Inst. of Technol., Pasadena, CA, USA (Sojoudi, S.)
Abstract	This work is concerned with solving non-convex power optimization problems by introducing the concept of “nonlinear optimization over graph”. To this end, the structure of a given nonlinear real/complex optimization with quadratic arguments is mapped into a generalized weighted graph, where each edge is associated with a weight set constructed from the known parameters of the optimization (e.g., the coefficients). This generalized weighted graph captures both the sparsity of the optimization and possible patterns in the coefficients. The notion of “sign definite sets” is introduced for both real and complex weight sets, and it is then shown that the polynomial-time solvability of the optimization may be inferred from the topology of its associated graph together with the sign definiteness of its weight sets. As an application of this result, it is finally proved that a broad class of optimization problems over power networks are polynomial-time solvable via two convex relaxations due to the passivity of transmission lines.
Sponsorship	IEEE Signal Process. Soc.
Starting Page	424
Ending Page	427
File Size	249633
Page Count	4
File Format	PDF
e-ISBN	9781467331463
DOI	10.1109/CAMSAP.2013.6714098
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2013-12-15
Publisher Place	France
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Power transmission lines Conferences Image edge detection Vectors Topology Computational complexity Optimization
Content Type	Text
Resource Type	Article

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