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applying a reduced gradient in quadratic programming

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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.

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References

  1. Murtagh, B.A. and Saunders, M.A., Large-Scale Linearly Constrained Optimization, Math. Programm., 1978, no. 14, pp. 41–72.

    Article  MATH  MathSciNet  Google Scholar 

  2. Murtagh, B., Sovremennoe lineinoe programmirovanie: teoriya i praktika (Advanced Linear Programming: Computation and Practice), Moscow: Mir, 1984.

    Google Scholar 

  3. Gill, P.E., Murray, W., and Wright, M., Prakticheskaya optimizatsiya (Practical Optimization), Moscow: Mir, 1985.

    Google Scholar 

  4. Wilkinson, J. and Reinsch, K., Spravochnik na yazyke ALGOL. Lineinaya algebra (ALGOL Language Handbook. Linear Algebra), Moscow: Mashinostroyenie, 1976.

    Google Scholar 

  5. 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.

    Article  MATH  MathSciNet  Google Scholar 

  6. 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.

  7. Hellerman, E. and Rarick, D.C., Reinversion with the Pressigned Pivot Procedure, Math. Programm., 1971, vol. 1, no. 2, pp. 195–216.

    Article  MATH  MathSciNet  Google Scholar 

  8. Mittelman, H.D., Decision Tree for Optimization Software, http://plato.asu.edu/guide.html.

  9. Martin, A., Achterberg, T., and Koch, T., MIPLIB—Mixed Integer Problem Library, 2003, http://miplib.zib.de.

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Original Russian Text © E.A. Kotel’nikov, 2010, published in Sibirskii Zhurnal Vychislitel’noi Matematiki, 2010, Vol. 13, No. 1, pp. 23–31.

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Kotel’nikov, E.A. applying a reduced gradient in quadratic programming. Numer. Analys. Appl. 3, 17–24 (2010). https://doi.org/10.1134/S1995423910010039

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  • DOI: https://doi.org/10.1134/S1995423910010039

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