Stability of Vector Problems of Integer Optimization: Relationship with the Stability of Sets of Optimal and Nonoptimal Solutions
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Several types of stability against perturbations of vector criterion coefficients are analyzed from the same point of view for a vector integer optimization problem with quadratic criterion functions. The concept of stability is defined. Necessary and sufficient conditions are formulated and analyzed for each type of stability. The topological structure of the sets of initial data on which some solution remains optimal is described.
Keywordsmulticriterion integer optimization partial quadratic criterion functions stability by vector-valued criterion perturbations of initial data
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- 1.I. V. Sergienko, L. N. Kozeratskaya, and T. T. Lebedeva, Stability and Parametric Analysis of Discrete Optimization Problems [in Russian], Naukova Dumka, Kiev (1995).Google Scholar
- 5.T. T. Lebedeva, N. V. Semenova, and T. I. Sergienko, “Criterion stability of vector problems of integer quadratic programming,” in: Theory of Optimal Solutions: A Collection of Scientific Papers [in Russian], Kiev, V. M. Glushkov Inst. Cybern. NASU, No. 2 (2003), pp. 140–146.Google Scholar
- 6.T. T. Lebedeva, N. V. Semenova, and T. I. Sergienko, “Optimality and solvability criteria in problems of linear optimization with a convex admissible set,” Dop. NANU, No. 10, 80–85 (2003).Google Scholar
- 8.T. T. Lebedeva, N. V. Semenova, and T. I. Sergienko, “Stability of vector integer optimization problems with quadratic criterion functions,” Theory of Stochastic Processes, 10(26), No. 34, 95–101 (2004).Google Scholar
- 9.V. V. Podinovskii and V. D. Nogin, Pareto-Optimal Solutions of Multicriteria Problems [in Russian], Nauka, Moscow (1982).Google Scholar
- 10.S. Smale, “Global analysis and economics, V. Pareto theory with constraints,” J. Math. Econ., No. 1, 213–221 (1974).Google Scholar