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Bednarczuk, Ewa M.

Continuity of minimal points with applications to parametric multiple objective optimization. (English) Zbl 1106.90064

Eur. J. Oper. Res. 157, No. 1, 59-67 (2004).
Summary: Basing ourselves on general results we investigate stability of Pareto points to finite-dimensional parametric multiple objective optimization problems (linear and/or convex).

Cited in 8 Documents

MSC:

90C29 Multi-objective and goal programming
90C31 Sensitivity, stability, parametric optimization

Keywords:

Multiple objective programming; Parametric programming; Stability analysis
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\textit{E. M. Bednarczuk}, Eur. J. Oper. Res. 157, No. 1, 59--67 (2004; Zbl 1106.90064)
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References:

[1] Azé, D.; Corvellec, J.-N., On the sensitivity of hoffman constants for systems of linear inequalities, SIAM journal of optimization, 12, 913-927, (2002) · Zbl 1014.65046
[2] Bank, B.; Guddat, J.; Klatte, D.; Kummer, B.; Tammer, K., Non-linear parametric optimization, (1982), Akademie-Verlag Berlin · Zbl 0502.49002
[3] Bednarczuk, E.M., Some stability results for vector optimization problems in partially ordered topological vector spaces, (), 2371-2382 · Zbl 0844.90073
[4] Bednarczuk, E.M., Upper hőlder continuity of minimal points, Journal on convex analysis, 9, 2, 327-338, (2002) · Zbl 1034.49028
[5] Bednarczuk, E.M., Hőlder-like properties of minimal points in vector optimization, Control and cybernetics, 31, 3, 423-438, (2002) · Zbl 1112.90371
[6] Bolintineanu, S.; El Maghri, M., Second-order efficiency conditions and sensitivity of efficient points, Journal of optimization theory and applications, 98, 3, 569-592, (1998) · Zbl 0915.90226
[7] Bonnans, J.F.; Shapiro, A., Perturbation analysis of optimization problems, (2000), Springer Verlag New York · Zbl 0966.49001
[8] Chen, G.Y.; Craven, B.D., Existence and continuity of solutions for vector optimization, Journal of optimization theory and applications, 81, 3, 459-468, (1994) · Zbl 0810.90112
[9] Davidson, M.P., Lipschitz continuity of Pareto optimal extreme points, Vestnik mosk. univ. ser. XV, 63, 41-45, (1996) · Zbl 0926.90082
[10] M.P. Davidson, Conditions for stability of a set of extreme points of a polyhedron and their applications, Technical Paper, Ross. Akad. Nauk, Vychisl. Centr, Moscow 1996
[11] Davidson, M.P., On the Lipschitz stability of weakly Slater systems of convex inequalitites, Vestnik mosk. univ. ser XV, 68, 24-28, (1998)
[12] Deng, S., Perturbation analysis of a condition number for convex inequality systems and global error bounds for analytic systems, Mathematical programming, 83, 265-282, (1998)
[13] Dontchev, A.L.; Zolezzi, T., ()
[14] Henig, M., The domination property in multicriteria optimization, Journal of optimization, theory and applications, 114, 7-16, (1986) · Zbl 0629.90084
[15] Holmes, R.B., Geometric functional analysis and its applications, (1975), Springer New York · Zbl 0336.46001
[16] Jahn, J., Mathematical vector optimization in partially ordered spaces, (1986), Peter Lang Frankfurt am Main · Zbl 0578.90048
[17] Levy, A.B., Scaled stability in variational problems, SIAM journal on optimization, 12, 861-874, (2002) · Zbl 1035.90089
[18] Levy, A.B., Solution sensitivity for general principles, SIAM journal on control and optimization, 40, 1-38, (2001) · Zbl 0985.90085
[19] Luc, D.T., Theory of vector optimization, (1989), Springer Verlag New York
[20] Peressini, A.L., Ordered topological vector spaces, (1967), Harper and Row New York · Zbl 0169.14801
[21] Petschke, M., On a theorem of arrow, barankin and blackwell, SIAM journal on control and optimization, 28, 395-401, (1990) · Zbl 0692.49005
[22] Schaefer, H., ()
[23] Sterna-Karwat, A., Convexity of the optimal multifunctions and its consequences in vector optimization, Optimization, 20, 799-807, (1989) · Zbl 0691.90080
[24] Tanino, T., Stability and sensitivity analysis in multiobjective nonlinear programming, Annals of operations research, 27, 97-114, (1990) · Zbl 0719.90065
[25] Tanino, T., Stability and sensitivity analysis in convex vector optimization, SIAM journal on control and optimization, 26, 521-536, (1988) · Zbl 0654.49011
[26] Tanino, T.; Sawaragi, Y.; Nakayama, H., Theory of multiobjective optimization, (1985), Academic Press New York · Zbl 0566.90053
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