Abstract
Relaxation methods have been recently shown to be very effective, for some large scale linear problems. The aim of this paper is to show that these procedures can be considerably improved by following a modified gradient step direction.
Partially supported by the Centro di Telecomunicazioni Spaziali of CNR (Italy). A provisional version of this work was presented at the International Conference on Operation Research (Eger, August 1974).
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
P.M. Camerini, L. Fratta and F. Maffioli, “A heuristically guided algorithm for the traveling salesman problem,” Journal of the Institution of Computer Science 4 (1973) 31–35.
P. M. Camerini and F. Maffioli, “Bounds for 3-matroid intersection problems,” Information Processing Letters 3 (1975) 81–83.
P.M. Camerini, L. Fratta and F. Maffioli, “Traveling salesman problem: heuristically guided search and modified gradient techniques,” to appear.
G.A. Croes, “A method for solving traveling salesman problems,” Operations Research 6 (1958) 791–812.
H. Crowder, “Computational improvements for subgradient optimization”, IBM Research Rept. RC 4907 (No. 21841) Thomas J. Watson Research Center (June 1974).
G.B. Dantzig, D.R. Fulkerson and S.M. Johnson, “Solution of a large scale traveling salesman problem,” Operations Research 2 (1954) 393–410.
J.B. Dantzig, Linear programming and extensions (Princeton University Press, Princeton, N.J., 1963) ch. 23.
M. Held and R.M. Karp, “A dynamic programming approach to sequencing problems,” SIAM Journal on Applied Mathematics 10 (1962) 195–210.
M. Held and R.M. Karp, “The traveling salesman problem and minimum spanning trees: part II,” Mathematical Programming 1 (1971) 6–25.
M. Held, R.M. Karp and P. Wolfe, “Large scale optimization and the relaxation methods,” in: Proceedings of the 25th Conference of the ACM, August 1972, pp. 507–509.
L.L. Karg and G.L. Thompson, “A heuristic approach to solving traveling salesman problems,” Management Science 10 (1964) 225–248.
S. Lin, “Computer solution of the traveling salesman problem,” The Bell System Technical Journal 44 (1965) 2245–2269.
F. Maffioli, “Shortest spanning hypertrees”, in: Symposium on optimization problems in engineering and economics, Naples, December 1974.
T. Motzkin and I.J. Schoenberg, “The relaxation method for linear inequalities,” Canadian Journal of Mathematics 6 (1954) 393–404.
J.F. Shapiro, “A decomposition algorithm for integer programming problems with many columns,” in: Proceedings of the 25th Conference of the ACM, August 1972, pp. 528–533.
P. Wolfe, M. Held and H. Crowder, “Validation of subgradient optimization,” Mathematical Programming 6 (1974) 62–88.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1975 The Mathematical Programming Society
About this chapter
Cite this chapter
Camerini, P.M., Fratta, L., Maffioli, F. (1975). On improving relaxation methods by modified gradient techniques. In: Balinski, M.L., Wolfe, P. (eds) Nondifferentiable Optimization. Mathematical Programming Studies, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120697
Download citation
DOI: https://doi.org/10.1007/BFb0120697
Received:
Revised:
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00763-7
Online ISBN: 978-3-642-00764-4
eBook Packages: Springer Book Archive