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- W3134417020 abstract "As a classic example of Khachiyan shows, some semidefinite programs (SDPs) have solutions whose size -- the number of bits necessary to describe them -- is exponential in the size of the input. Exponential size solutions are the main obstacle to solve a long standing open problem: can we decide feasibility of SDPs in polynomial time? We prove that large solutions are actually quite common in SDPs: a linear change of variables transforms every strictly feasible SDP into a Khachiyan type SDP, in which the leading variables are large. As to large, that depends on the singularity degree of a dual problem. Further, we present some SDPs in which large solutions appear naturally, without any change of variables. We also partially answer the question: how do we represent such large solutions in polynomial space?" @default.
- W3134417020 created "2021-03-15" @default.
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- W3134417020 date "2021-02-26" @default.
- W3134417020 modified "2023-09-27" @default.
- W3134417020 title "How do exponential size solutions arise in semidefinite programming" @default.
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