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In this paper, we establish sufficient conditions for the solution set of parametric generalized vector mixed quasivariational inequality problem to have the semicontinuities such as the inner-openness, lower semicontinuity and Hausdorff lower semicontinuity. Moreover, a key assumption is introduced by virtue of a parametric gap function by using a nonlinear scalarization function. Then, by using the key assumption, we establish condition (Hh( γ0, λ0, μ0)) is a sufficient and necessary condition for the Hausdorff lower semicontinuity, continuity and Hausdorff continuity of the solution set for this problem in Hausdorff topological vector spaces with the objective space being infinite dimensional. The results presented in this paper are different and extend from some main results in the literature.
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참고문헌 (26)
참고문헌 신청
B. T. Kien / 2005 / On the lower semicontinuity of optimal solution sets / Optimization 54 (2) : 123 ~ 130
C. Berge / 1963 / Topological Spaces / Oliver and Boyd
C. R. Chen / 2010 / On the solution semicontinuity to a parametric generalized vector quasivariational inequality / Comput. Math. Appl 60 (8) : 2417 ~ 2425
C. S. Lalitha / 2011 / Sta
F. Giannessi / 1980 / Variational Inequalities and Complementarity Problems / Wiley : 151 ~ 186
C. Berge / 1963 / Topological Spaces / Oliver and Boyd
C. R. Chen / 2010 / On the solution semicontinuity to a parametric generalized vector quasivariational inequality / Comput. Math. Appl 60 (8) : 2417 ~ 2425
C. S. Lalitha / 2011 / Sta
F. Giannessi / 1980 / Variational Inequalities and Complementarity Problems / Wiley : 151 ~ 186
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