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• W3168285534 abstract "We investigate the approximability of the following optimization problem. The input is an n× n matrix A=(Aij) with real entries and an origin-symmetric convex body K⊂ ℝn that is given by a membership oracle. The task is to compute (or approximate) the maximum of the quadratic form ∑i=1n∑j=1n Aij xixj=⟨ x,Ax⟩ as x ranges over K. This is a rich and expressive family of optimization problems; for different choices of matrices A and convex bodies K it includes a diverse range of optimization problems like max-cut, Grothendieck/non-commutative Grothendieck inequalities, small set expansion and more. While the literature studied these special cases using case-specific reasoning, here we develop a general methodology for treatment of the approximability and inapproximability aspects of these questions." @default.
• W3168285534 created "2021-06-22" @default.
• W3168285534 creator A5052985577 @default.
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• W3168285534 date "2021-06-15" @default.
• W3168285534 modified "2023-09-27" @default.
• W3168285534 title "A framework for quadratic form maximization over convex sets through nonconvex relaxations" @default.
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• W3168285534 doi "https://doi.org/10.1145/3406325.3451128" @default.
• W3168285534 hasPublicationYear "2021" @default.
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