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A Note on the Convexity of logdet(I+KX−1...

Kim, Kwang-Ki K....

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A Note on the Convexity of logdet(I+KX−1) and its Constrained Optimization Representation by Kim, Kwang-Ki K. ( Author )

Content Provider	Lemonjar Open Access
Publisher	N.A
Publication Date	02-09-2015
Summary	This note provides another proof for the {\em convexity} ({\em strict convexity}) of logdet(I+KX−1) over the positive definite cone for any given positive semidefinite matrix K⪰0 (positive definite matrix K≻0) and the {\em strictly convexity} of logdet(K+X−1) over the positive definite cone for any given K⪰0. Equivalent optimization representation with linear matrix inequalities (LMIs) for the functions logdet(I+KX−1) and logdet(K+X−1) are presented. Their optimization representations with LMI constraints can be particularly useful for some related synthetic design problems.
ISBN	-
Item Type	Article
File Type	pdf
File Size	36.88 KB
Language	English
Subjects	-
Unlimited	MYR 0.00
Total read	-
URL	https://arxiv.org/abs/1509.00777

Citation

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AMA 11th EditionReferences

Kim, Kwang-Ki K.. A Note on the Convexity of logdet(I+KX−1) and its Constrained Optimization Representation. N.A. September 02, 2015. Accessed August 14, 2025. https://online.provdatabase.com/cite/11317

APA 7th EditionReferences

Kim, Kwang-Ki K.. (2015). A Note on the Convexity of logdet(I+KX−1) and its Constrained Optimization Representation. N.A. https://online.provdatabase.com/cite/11317

Chicago 17th EditionReferences

Kim, Kwang-Ki K.. A Note on the Convexity of logdet(I+KX−1) and its Constrained Optimization Representation. N.A. 2015. https://online.provdatabase.com/cite/11317

HarvardReferences

Kim, Kwang-Ki K.. (2015). A Note on the Convexity of logdet(I+KX−1) and its Constrained Optimization Representation. [Online]. N.A. Available from: https://online.provdatabase.com/cite/11317. (Accessed 14 August 2025).

Harvard AustraliaReferences

Kim, Kwang-Ki K., 2015, A Note on the Convexity of logdet(I+KX−1) and its Constrained Optimization Representation, N.A, viewed 14 August 2025, <https://online.provdatabase.com/cite/11317>

MLA 9th EditionWorks Cited

Kim, Kwang-Ki K.. A Note on the Convexity of logdet(I+KX−1) and its Constrained Optimization Representation. N.A, 2015. PROV Database, https://online.provdatabase.com/cite/11317.

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