Abstract
This paper considers specific aspects of implementing an algorithm for solving problems of quadratic programming, which is based on a reduced gradient method. In the subspace of superbasis variables, minimization is carried out by a conjugate gradient method. Some examples of solving test problems are given.
Similar content being viewed by others
References
Murtagh, B.A. and Saunders, M.A., Large-Scale Linearly Constrained Optimization, Math. Programm., 1978, no. 14, pp. 41–72.
Murtagh, B., Sovremennoe lineinoe programmirovanie: teoriya i praktika (Advanced Linear Programming: Computation and Practice), Moscow: Mir, 1984.
Gill, P.E., Murray, W., and Wright, M., Prakticheskaya optimizatsiya (Practical Optimization), Moscow: Mir, 1985.
Wilkinson, J. and Reinsch, K., Spravochnik na yazyke ALGOL. Lineinaya algebra (ALGOL Language Handbook. Linear Algebra), Moscow: Mashinostroyenie, 1976.
Forrest, J.J. and Tomlin, J.A., Updated Triangular Factors of the Basis to Maintain Sparsity in the Product Form Simplex Method, Math. Programm., 1972, vol. 2, no. 3, pp. 263–278.
Zabinyako, G.I., Kotel’nikov, E.A., Kobkova, T.M., and Rozhin, V.E., Programmy lineinogo program-mirovaniya LP-VTs (LP-VTs Linear Programming Programs), Novosibirsk, 1995.
Hellerman, E. and Rarick, D.C., Reinversion with the Pressigned Pivot Procedure, Math. Programm., 1971, vol. 1, no. 2, pp. 195–216.
Mittelman, H.D., Decision Tree for Optimization Software, http://plato.asu.edu/guide.html.
Martin, A., Achterberg, T., and Koch, T., MIPLIB—Mixed Integer Problem Library, 2003, http://miplib.zib.de.
Author information
Authors and Affiliations
Additional information
Original Russian Text © E.A. Kotel’nikov, 2010, published in Sibirskii Zhurnal Vychislitel’noi Matematiki, 2010, Vol. 13, No. 1, pp. 23–31.
Rights and permissions
About this article
Cite this article
Kotel’nikov, E.A. applying a reduced gradient in quadratic programming. Numer. Analys. Appl. 3, 17–24 (2010). https://doi.org/10.1134/S1995423910010039
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1995423910010039