On the quasistability of trajectory problems of vector optimization. (English. Russian original) Zbl 0912.90244
Math. Notes 63, No. 1, 19-24 (1998); translation from Mat. Zametki 63, No. 1, 21-27 (1998).
Summary: We consider quasistable multicriteria problems of discrete optimization on systems of subsets (trajectory problems). We single out the class of problems for which new Pareto optima can appear, while other optima for the problems do not disappear when the coefficients of the objective functions are slightly perturbed (in the Chebyshev metric). For the case of linear criteria (MINSUM), we obtain a formula for calculating the quasistability radius of the problem.
References:
| [1] | J. Hadamard,Sur les problèmes aux derivées partielles et leur signification partielle et leur signification physique, Bulletin, Princeton Univ. (1902). |
| [2] | D. A. Molodtsov and V. V. Fedorov, ”Stability of optimality principles” in:Modern State of Operations Analysis [in Russian], Nauka, Moscow (1979), pp. 236–263. |
| [3] | Mathematical Optimization: Questions of Solvability and Stability (E. G. Belousov and B. Bank, editors) [in Russian], Izd. Moskov. Univ., Moscow (1986). |
| [4] | Yu. A. Dubov, S. I. Travkin, and V. N. Yakimets,Multicriteria Models for Formation and for Choice of Variants of Systems [in Russian], Nauka, Moscow (1986). · Zbl 0664.90047 |
| [5] | D. A. Molodtsov,Stability of Optimality Principles [in Russian], Nauka, Moscow (1987). · Zbl 0632.49001 |
| [6] | L. N. Kozeratskaya, T. T. Lebedeva, and I. V. Sergienko, ”Investigations of stability of problems of discrete optimization,”Kibernetika i Sistemnyi Analiz [in Russian], No. 3, 78–93 (1993). · Zbl 0829.90118 |
| [7] | I. V. Sergienko, L. N. Kozeratskaya, and T. T. Lebedeva,Investigations of Stability and Parametric Analysis of Discrete Optimization Problems [in Russian], Navukova dumka, Kiev (1995). · Zbl 0864.90096 |
| [8] | V. K. Leont’ev, ”Stability of the problem of traveling salesman,”Zh. Vychisl. Mat. i Mat. Fiz. [U.S.S.R. Comput. Math. and Math. Phys.],15, No. 5, 1298–1309 (1975). |
| [9] | Yu. N. Sotskov, V. K. Leontev, and E. N. Gordeev, ”Some concepts of stability analysis in combinatorial optimization,”Discrete Appl. Math.,58, 169–190 (1995). · Zbl 0833.90098 · doi:10.1016/0166-218X(93)E0126-J |
| [10] | É. N. Gordeev and V. K. Leont’ev, ”A general approach to investigation of stability for solutions of discrete optimization problems,”Zh. Vychisl. Mat. i Mat. Fiz. [Comput. Math. and Math. Phys.],36, No. 1, 66–72 (1996). |
| [11] | V. A. Emelichev and M. K. Kravtsov, ”On stability of trajectory problems of vector optimization,”Kibernetika i sistemnyi analiz, No. 4, 137–143 (1995). |
| [12] | L. N. Kozeratskaya, T. T. Lebedeva, and T. I. Sergienko, ”Problems of integer programming with a vector criterion: parametric analysis and investigation of stability,”Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.],307, No. 3, 527–529 (1989). · Zbl 0695.90066 |
| [13] | V. V. Podinovskii and V. D. Nogin,Pareto-Optimal Solutions of Multicriteria Problems [in Russian], Nauka, Moscow (1982). |
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