Regularization of a lexicographic vector problem of integer programming
A stability criterion for a vector integer linear problem of lexicographic optimization is obtained. A regularization method is proposed that allows us to reduce a possible unstable output problem to a sequence of perturbed stable equivalent problems.
Keywordsstability radius problem of integer linear programming lexicographic optimization perturbed stable problem
Unable to display preview. Download preview PDF.
- 1.L. N. Kozeratrskaya, T. T. Lebedeva, and T. I. Sergienko, “Regularization of problems of integer vector optimization,” Kibern. Sist. Anal., No. 3, 172–176 (1993).Google Scholar
- 2.T. I. Sergienko, L. N. Kozeratskaya, and T. T. Lebedeva, Stability Study and Parametric Analysis of Discrete Optimization Problems [in Russian], Naukova Dumka, Kiev (1995).Google Scholar
- 4.D. A. Molodtsov, “On sequential optimization,” in: Vopr. Prikl. Mat. [in Russian], Irkutsk (1975), pp. 71–84.Google Scholar
- 5.D. A. Molodtsov and V. V. Fedorov, “Stability of optimality principles,” in: State of the Art of the Theory of Operations Research [in Russian], Nauka, Moscow (1979), pp. 236–262.Google Scholar
- 7.I. V. Sergienko, Mathematical Models and Methods of Solving Problems of Discrete Optimization [in Russian], Naukova Dumka, Kiev (1988).Google Scholar
- 8.R. A. Berdysheva and V. A. Emelichev, “Stability of linear path problems in lexicographic optimization,” Kibern. Sist. Anal., No. 4, 83–88 (1997).Google Scholar
- 9.V. A. Emelichev and R. A. Berdysheva, “The radius of pseudostability, quasistability, and stability of a vector trajectory problem of lexicographic optimization,” Diskr. Mat.,10, No. 1, 20–27 (1998).Google Scholar