# On Quadratic Programming with a Ratio Objective

@inproceedings{Bhaskara2011OnQP,
title={On Quadratic Programming with a Ratio Objective},
booktitle={International Colloquium on Automata, Languages and Programming},
year={2011}
}
• Published in
International Colloquium on…
9 January 2011
• Computer Science, Mathematics
Quadratic Programming (QP) is the well-studied problem of maximizing over {−1,1} values the quadratic form ∑i≠jaijxixj. QP captures many known combinatorial optimization problems, and assuming the Unique Games conjecture, Semidefinite Programming (SDP) techniques give optimal approximation algorithms. We extend this body of work by initiating the study of Quadratic Programming problems where the variables take values in the domain {−1,0,1}. The specific problem we study is \begin{aligned… • Computer Science STOC • 2017 This work shows that if P is δ-close to supporting a t-wise uniform distribution on satisfying assignments, then the degree-Θ(n/Δ2/(t - 1) logΔ) SOS algorithm cannot (δ+o(1))-refute a random instance of CSP(P). This thesis studies refutation using sum-of-squares (SOS) proof systems using a sequence of increasingly powerful proof systems parameterized by degree: the higher the degree, the more powerful the proof system. • Mathematics, Computer Science • 2012 The best known algorithm for the so-called densest k-subgraph problem is presented, which gives roughly an n1/4 factor approximation, and it is proved that without such a restriction, the problem is hard to approximate to an almost polynomial factor. • Mathematics • 2013 What can we say about the spectra of a collection of microscopic variables when only their coarse-grained sums are experimentally accessible? In this paper, using the tools and methodology from the • Mathematics • 2011 What can we say about the spectra of a collection of microscopic variables when only their coarse-grained sums are experimentally accessible? In this paper, using the tools and methodology from the • Computer Science NeurIPS • 2020 This paper derives a novel formulation in which each conﬂicting group is naturally characterized by the solution to the maximum discrete Rayleigh’s quotient ( M AX -DRQ ) problem, and presents two spectral methods for approximate solutions to the problem. • Computer Science, Mathematics • 2015 In this paper, an alternative method for Wolfe’s modified simplex method is introduced. This method is easy to solve quadratic programming problem (QPP) concern with non-linear programming problem • Computer Science, Mathematics • 2015 This paper adds to the rich evidence for the versatility of copositive optimization approaches, and hints at possible novel approximation strategies combining continuous and discrete optimization techniques in the domain of (fractional) polynomial optimization. ## References SHOWING 1-10 OF 29 REFERENCES • Mathematics Math. Program. • 1999 It is shown that this bound is sharp in order, as far as the dependence on m is concerned, and that a~feasible solution x to (P) with x^TAx\ge \frac{{\Opt(\hbox{{\rm SDP}})}}{{2\ln(2m^2)}} \eqno{(*)} can be found efficiently.
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