Tính nửa liên tục từ dưới của ánh xạ nghiệm tối ưu trong tối ưu hóa véc tơ nửa vô hạn

Journal of Systems Science and Complexity - Tập 28 - Trang 1312-1325 - 2015
Xunhua Gong1
1Department of Mathematics, Nanchang University, Nanchang, China

Tóm tắt

Bài báo này thiết lập một số điều kiện đủ cho tính nửa liên tục từ dưới của ánh xạ nghiệm hiệu quả đối với bài toán tối ưu hóa véc tơ nửa vô hạn với sự nhiễu của cả hàm mục tiêu và tập ràng buộc trong các không gian tuyến tính chuẩn. Tập ràng buộc là tập hợp các nghiệm yếu hiệu quả của bài toán cân bằng véc tơ, và được làm nhiễu thông qua sự nhiễu của ánh xạ tiêu chí đối với bài toán cân bằng véc tơ.

Từ khóa

#tối ưu hóa véc tơ #ánh xạ nghiệm #nửa liên tục #bài toán cân bằng véc tơ

Tài liệu tham khảo

Naccache P H, Stability in multicriteria optimization, Journal of Mathematic Analysis and Applications, 1979, 68: 441–3. Tanino T and Sawaragi Y, Stability of nondominated solutions in multicriteria decision-making, Journal of Optimization Theory and Applications, 1980, 30: 229–3. Penot J P and Sterna-Karwat A, Parametrized multicriteria optimization: Continuity and closedness of optimal multifunctions, Journal of Mathematic Analysis and Applications, 1986, 120: 150–3. Bednarczuk E M, Berge-Type theorems for vector optimization problems, Optimization, 1995, 32: 373–3. Bednarczuk E M, A note on lower semicontinuity of minimal points, Nonlinear Analysis, 2002, 50: 285–3. Chuong T D, Yao J C, and Yen N D, Further results on the lower semicontinuity of efficient point multifunctions, Pacific Journal of Optimization, 2010, 6: 405–3. Xiang S W and Zhou Y H, Continuity properties of solutions of vector optimization, Nonlinear Analysis, 2006, 64: 2496–3. Todorov M I, Kuratowski convergence of the efficient sets in the parametric linear vector semiinfinite optimization, European Journal of Operational Research, 1996, 94: 610–3. Chuong T D, Huy N Q, and Yao J C, Pseudo-Lipschitz property of linear semi-infinite vector optimization problems, European Journal of Operational Research, 2010, 200: 639–3. Chuong T D and Yao J C, Sufficient conditions for pseudo-Lipschitz property in convex semiinfinite vector optimization problems, Nonlinear Analysis, 2009, 71: 6312–3. Chuong T D, Lower semicontinuity of the Pareto solution map in quasiconvex semi-infinite vector optimization, Journal of Mathematic Analysis and Applications, 2012, 388: 443–3. Chuong T D, Huy N Q, and Yao J C, Stability of semi-infinite vector optimization problems under functional perturbations, Journal of Global Optimization, 2009, 45: 583–3. Luc D T, Theory of Vector Optimization, Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, New York, 1989, 319. Gong X H, Connectedness of the solution sets and scalarization for vector equilibrium problems, Journal of Optimization Theory and Applications, 2007, 133: 151–3. Göpfert A, Riahi H, Tammer C, and Zǎlinescu C, Variational Methods in Partially Ordered Spaces, Springer-Verlag, New York, 2003. Aubin J P and Ekeland I, Applied Nonlinear Analysis, New York, John Wiley & Son, 1984. Fan K, A generalization of Tychonoff’s fixed point theorem, Mathematics Analysis, 1961, 142: 305–3. Gong X H, Continuity of the solution set to parametric weak vector equilibrium problems, Journal of Optimization Theory and Applications, 2008, 139: 35–3. Gong X H and Yao Y J, Lower semicontinuity of the set of efficient solutions for generalized systems, Journal of Optimization Theory and Applications, 2008, 138: 197–3. Chen B and Gong X H, Continuity of the solution set to parametric set-valued weak vector equilibrium problems, Pacific Journal of Optimization, 2010, 6: 511–3. Li S J and Fang Z M, Lower semicontinuity of the solution mappings to a parametric generalized Ky Fan inequality, Journal of Optimization Theory and Applications, 2010, 147: 507–3. Peng Z Y, Yang X M, and Peng J W, On the lower semicontinuity of the solution mappings to parametric weak generalized Ky Fan inequality, Journal of Optimization Theory and Applications, 2012, 152: 256–3. Jahn J, Mathematical Vector Optimization in Partially-Ordered Linear Spaces, Germany: Peter Lang, Frankfurt an Main, 1986.