Lossless Convexification and Duality

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The main goal of this paper is to investigate strong duality of non-convex semidefinite programming problems (SDPs). In the optimization community, it is well-known that a convex optimization problem satisfies strong duality if the Slater's condition holds. However, this result cannot be directly generalized to non-convex problems. In this paper, we prove that a class of non-convex SDPs with special structures satisfies strong duality under the Slater's condition. Such a class of SDPs arises in SDP-based control analysis and design approaches. Throughout the paper, several examples are given to support the proposed results. We expect that the proposed analysis can potentially deepen our understanding of non-convex SDPs arising in the control community, and promote their analysis based on KKT conditions.
Publisher
Elsevier
Issue Date
2024-09
Language
English
Citation

Journal of the Franklin Institute

ISSN
0016-0032
DOI
10.48550/arXiv.2108.01457
URI
http://hdl.handle.net/10203/322398
Appears in Collection
EE-Journal Papers(저널논문)
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