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• W3122365788 abstract "In recent literature, many successful attempts have been made in reformulating non-convex optimization problems as convex conic optimization problems, or at least in giving powerful relaxations of this type. However, it is often the case that these approaches suffer from poor computational performance due to the size of the reformulation. In this paper we study QCQPs whose special structure allows for a reduced conic relaxation where the variables are lifted into a smaller space compared to traditional approaches. We show that in special cases these relaxations are exact reformulations. We contextualized these results in the field of matrix completion in two ways. First we derive an exact reformulation of the QCQPs that is based on the geometry of the cone of partial arrowhead matrix that have a set-completely positive completion. However, we do not reference the completability in the proof, but instead rely purely on geometric aspects. We also show, that our reduced conic reformulation can be seen as relaxation of the latter exact reformulation and describe the gap between those two in terms of the difference of two subsets of a space that is isomorphic to the space of arrowhead matrices if a certain type. Second we show that our partial exactness results imply a new sufficient conditions for set-completely positive matrix completion." @default.
• W3122365788 created "2021-02-01" @default.
• W3122365788 creator A5055915468 @default.
• W3122365788 date "2021-01-15" @default.
• W3122365788 modified "2023-09-27" @default.
• W3122365788 title "On reduced, conic reformulations of QCQPs and set-completely positive matrix completion" @default.
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• W3122365788 hasPublicationYear "2021" @default.
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