Abstract
This paper establishes a set of necessary and sufficient conditions in order that a vectorx be a local minimum point to the general (not necessarily convex) quadratic programming problem:
minimizep T x + 1/2x T Qx, subject to the constraintsHx ≧ h.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A.V. Fiacco, “Second order sufficient conditions for weak and strict constrained minima,”SIAM Journal of Applied Mathematics 16 (1968) 105–108.
F. John, “Extremum problems with inequalities as subsidiary conditions”,Studies and essays (Interscience. New York, 1948) pp. 187–204.
H.W. Kuhn and A.W. Tucker,Nonlinear Programming, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (University of California Press, Berkeley, California, 1951) pp. 481–492.
C. McCormick, “Second order optimality conditions for constrained minima,”SIAM Journal on Applied Mathematics 15 (1967) 641–652.
A. Orden, “Stationary points of quadratic functions under linear constraints,”The Computer Journal 7 (1964) 238–242.
K. Ritter, “Stationary points of quadratic maximum problems,”Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 4 (1965) 149–158.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Majthay, A. Optimality conditions for quadratic programming. Mathematical Programming 1, 359–365 (1971). https://doi.org/10.1007/BF01584097
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01584097