Semidefinite programming: Difference between revisions

Revision as of 18:11, 31 December 2023

Revision as of 15:58, 1 January 2024

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{{Short description|Subfield of convex optimization}}

'''Semidefinite programming''' ('''SDP''') is a subfield of [[convexmathematical optimizationprogramming]] concerned with the optimization of a linear [[objective function]] (a user-specified function that the user wants to minimize or maximize)

over the intersection of the [[Cone (linear algebra)|cone]] of [[Positive-definite matrix#Negative-definite, semidefinite and indefinite matrices|positive semidefinite]] [[Matrix (mathematics)|matrices]] with an [[affine space]], i.e., a [[spectrahedron]].<ref name=":0">{{Citation |last=Gärtner |first=Bernd |title=Semidefinite Programming |date=2012 |url=https://doi.org/10.1007/978-3-642-22015-9_2 |work=Approximation Algorithms and Semidefinite Programming |pages=15–25 |editor-last=Gärtner |editor-first=Bernd |access-date=2023-12-31 |place=Berlin, Heidelberg |publisher=Springer |language=en |doi=10.1007/978-3-642-22015-9_2 |isbn=978-3-642-22015-9 |last2=Matoušek |first2=Jiří |editor2-last=Matousek |editor2-first=Jiri}}</ref>