Approximation Algorithms for Quadratic Programming

AbstractWe consider the problem of approximating the global minimum of a general quadratic program (QP) with n variables subject to m ellipsoidal constraints. For m=1, we rigorously show that an ∈-minimizer, where error ∈ ∈ (0, 1), can be obtained in polynomial time, meaning that the number of arithmetic operations is a polynomial in n, m, and log(1/∈). For m ≥ 2, we present a polynomial-time (1- $$\frac{1}{{m^2 }}$$ )-approximation algorithm as well as a semidefinite programming relaxation for this problem. In addition, we present approximation algorithms for solving QP under the box constraints and the assignment polytope constraints.

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