ON THE UPPER SEMICONTINUITY OF SOLUTION MAPPINGS FOR PARAMETRIC WEAK VECTOR BILEVEL EQUILIBRIUM PROBLEMS
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Abstract
This paper examines parametric weak vector bilevel equilibrium problems. The sufficient conditions of upper semicontinuity, Hausdorff upper semicontinuity, and closedness of solution mappings for this problem were established. Our main results, Theorme 3.1 and Theorem 3.5 are new. Some examples are given to illustrate the results.
Keywords
bilevel equilibrium problems, upper semicontinuity, Hausdorff upper semicontinuity, closedness
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References
Aubin, J. P., & Ekeland, I. (1984). Applied Nonlinear Analysis. New York: John Wiley and Sons.
Blum, E., & Oettli, W. (1994). From optimization and variational inequalities to equilibrium problems. Mathematic. Student-India, 63, 123-145.
Bui, T. K. (2005). On the lower semicontinuity of optimal solution sets. Optimization, 54, 123-130.
Dinh, T. L. (1989). Theory of Vector Optimization: Lecture Notes in Economics and Mathematical Systems. Springer-Verlag Berlin Heidelberg.
Lalitha, C. S., & Bhatia, G. (2011), Stability of parametric quasivariational inequality of the Minty type. Journal of Optimization Theory and Applications, 148, 281-300.
Lam, Q. A., & Nguyen, V. H (2018a). Stability of solution mappings for parametric bilevel vector equilibrium problems. Computational & Applied Mathematics, 37, 1537-1549.
Lam, Q. A., & Nguyen, V. H (2018b). Gap functions and Hausdorff continuity of solution mappings to parametric strong vector quasiequilibrium problems. Journal of Industrial and Management Optimization, 14, 65-79.
Nguyen, V. H. (2018). On the stability of the solution mapping for parametric traffic network problems. Indagationes Mathematicae, 29, 885-894.
Blum, E., & Oettli, W. (1994). From optimization and variational inequalities to equilibrium problems. Mathematic. Student-India, 63, 123-145.
Bui, T. K. (2005). On the lower semicontinuity of optimal solution sets. Optimization, 54, 123-130.
Dinh, T. L. (1989). Theory of Vector Optimization: Lecture Notes in Economics and Mathematical Systems. Springer-Verlag Berlin Heidelberg.
Lalitha, C. S., & Bhatia, G. (2011), Stability of parametric quasivariational inequality of the Minty type. Journal of Optimization Theory and Applications, 148, 281-300.
Lam, Q. A., & Nguyen, V. H (2018a). Stability of solution mappings for parametric bilevel vector equilibrium problems. Computational & Applied Mathematics, 37, 1537-1549.
Lam, Q. A., & Nguyen, V. H (2018b). Gap functions and Hausdorff continuity of solution mappings to parametric strong vector quasiequilibrium problems. Journal of Industrial and Management Optimization, 14, 65-79.
Nguyen, V. H. (2018). On the stability of the solution mapping for parametric traffic network problems. Indagationes Mathematicae, 29, 885-894.