UDC 519.8
1 V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine
 lebedevatt@gmail.com
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2 V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine
nvsemenova@meta.ua
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3 V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine
taniaser62@gmail.com
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MULTI-OBJECTIVE OPTIMIZATION PROBLEM: STABILITY WITH RESPECT
TO INITIAL DATA PERTURBATIONS IN VECTOR CRITERION
Abstract. The conditions of stability with respect to initial data perturbations in vector criterion for multi-objective optimization problem with continuous partial criterion functions and feasible set of arbitrary structure are established. The sufficient and necessary conditions of three types of stability for the problem of finding Pareto-optimal solutions are proved.
Keywords: vector optimization problem, vector criterion, stability, Pareto optimal solutions, Slater set, Smale set, perturbations of initial data.
FULL TEXT
REFERENCES
- Kozeratskaya L.N., Lebedeva T.T., Sergienko T.I. Mixed integer vector optimization: Stability issues. Cybernetics and Systems Analysis. 1991. Vol. 27, N 1. P. 76–80.
- Kozeratskaya L.N. Vector optimization problems: Stability in the decision space and in the space of alternatives. Cybernetics and Systems Analysis. 1994. Vol. 30, N 6. P. 891–899.
- Sergienko I.V., Kozeratskaya L.N., Lebedeva T.T. Stability study and parametric analysis of discrete optimization problems [in Russian]. Kiev: Nauk. dumka, 1995. 170 p.
- Lebedeva T.T., Semenova N.V., Sergienko T.I. Stability of vector problems of integer optimization: Relationship with the stability of sets of optimal and nonoptimal solutions. Cybernetics and Systems Analysis. 2005. Vol. 41, N 4. P. 551–558.
- Lebedeva T.T., Sergienko T.I. Stability of a vector integer quadratic programming problem with respect to vector criterion and constraints. Cybernetics and Systems Analysis. 2006. Vol. 42, N 5. P. 667–674.
- Lebedeva T.T., Sergienko T.I. Different types of stability of vector integer optimization problem: General approach. Cybernetics and Systems Analysis. 2008. Vol. 44, N 3. P. 429–433.
- Lebedeva T.T., Semenova N.V., Sergienko T.I. Qualitative characteristics of the stability vector discrete optimization problems with different optimality principles. Cybernetics and Systems Analysis. 2014. Vol. 50, N 2. P. 228–233.
- Sergienko I.V., Lebedeva T.T., Semenova N.V. Existence of solutions in vector optimization problems. Cybernetics and Systems Analysis. 2000. Vol. 36, N 6. P. 823–828.
- Sergienko T.I. Conditions of Pareto optimization problems solvability. Stable and unstable solvability. In: Optimization Methods and Applications. Springer Optimization and Its Applications. Butenko S., Pardalos P., Shylo V. (Eds.). Cham: Springer, 2017. Vol. 130. P. 457–464.
- Emelichev V.A., Kuzmin K.G. Stability radius of a vector integer linear programming problem: Case of a regular norm in the space of criteria. Cybernetics and Systems Analysis. 2010. Vol. 46, N 1. P. 72–79.
- Emelichev V.A., Kotov V.M., Kuzmin K.G., Lebedeva T.T., Semenova N.V., Sergienko T.I. Stability and effective algorithms for solving multiobjective discrete optimization problems with incomplete information. Journal of Automation and Information Sciences. 2014. Vol. 46, N 2. P. 27–41.
- Emelichev V., Nikulin Yu. On the quasistability radius for a multicriteria integer linear programming problem of finding extremum solutions. Cybernetics and Systems Analysis. 2019. Vol. 55, N 6. P. 949–957.
- Podinovsky V.V., Nogin V.D. Pareto-optimal solutions to multicriteria problems [in Russian]. Moscow: Naka, 1982. 256 p.
- Lyashko I.I., Emelyanov V.F., Boyarchuk O.K. Mathematical analysis. Part 1 [in Ukrainian]. Kyiv: Vyshcha shk., 1992. 495 p.
