Maximization of a Convex Quadratic Form on a Polytope: Factorization and the Chebyshev Norm Bounds
Maximization of a convex quadratic form on a convex polyhedral set is an NP-hard problem. We focus on computing an upper bound based on a factorization of the quadratic form matrix and employment of the maximum vector norm. Effectivity of this approach depends on the factorization used. We discuss several choices as well as iterative methods to improve performance of a particular factorization. We carried out numerical experiments to compare various alternatives and to compare our approach with other standard approaches, including McCormick envelopes.
KeywordsConvex quadratic form Relaxation NP-hardness Interval computation
- 3.Bazaraa, M.S., Sherali, H.D., Shetty, C.M.: Nonlinear Programming. Theory and Algorithms. 3rd edn. Wiley, Hoboken (2006)Google Scholar
- 5.Floudas, C.A.: Deterministic Global Optimization. Theory, Methods and Applications, Nonconvex Optimization and its Applications, vol. 37. Kluwer, Dordrecht (2000)Google Scholar
- 7.Gould, N.I.M., Toint, P.L.: A quadratic programming bibliography. RAL Internal Report 2000-1, Science and Technology Facilities Council, Scientific Computing Department, Numerical Analysis Group, 28 March, 2012. ftp://ftp.numerical.rl.ac.uk/pub/qpbook/qp.pdf