We 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 - 1/m2)-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.
Bibliographical noteFunding Information:
⁄Supported by the Australian Research Council. †Supported in part by the Department of Management Sciences of the University of Iowa where he performed this research during a research leave, and by the Natural Sciences and Engineering Research Council of Canada under grant OPG0090391. ‡Supported in part by NSF grants DDM-9207347 and DMI-9522507, and by the Iowa Business School Summer Grant.
- Global minimizer
- Polynomial-time approximation algorithm
- Quadratic programming