Abstract
In the paper, we study the generalized differentiability in set-valued optimization, namely stydying the second-order composed radial derivative of a given set-valued mapping. Inspired by the adjacent cone and the higher-order radial con in Anh NLH et al. (2011), we introduce the second-order composed radial derivative. Then, its basic properties are investigated and relationships between the second-order compsoed radial derivative of a given set-valued mapping and that of its profile are obtained. Finally, applications of this derivative to sensitivity analysis are studied. In detail, we work on a parametrized set-valued optimization problem concerning Pareto solutions. Based on the above-mentioned results, we find out sensitivity analysis for Pareto solution mapping of the problem. More precisely, we establish the second-order composed radial derivative for the perturbation mapping (here, the perturbation means the Pareto solution mapping concerning some parameter). Some examples are given to illustrate our results. The obtained results are new and improve the existing ones in the literature.
Highlights
In the paper, we study the generalized differentiability in set-valued optimization, namely stydying the second-order composed radial derivative of a given set-valued mapping
Inspired by the adjacent cone and the higher-order radial con in Anh NLH et al. (2011), we introduce the second-order composed radial derivative
Based on the above-mentioned results, we find out sensitivity analysis for Pareto solution mapping of the problem
Summary
TÓM TẮT Trong bài báo này, chúng tôi nghiên cứu về tính khả vi suy rộng trong tối ưu đa trị, cụ thể là nghiên cứu về đạo hàm theo tia cấp hai dạng hợp của một ánh xạ đa trị cho trước. Vào năm 2017, Xu và Peng dùng đạo hàm tiếp xúc cấp cao thiết lập kết quả về phân tích độ nhạy cho ánh xạ nhiễu proper theo kiểu Henig [18]. Xuất phát từ ý tưởng của các kết quả nghiên cứu trước đây [9, 11, 13, 17, 18], trong bài báo này chúng tôi dùng đạo hàm theo tia cấp hai dạng hợp trong phân tích độ nhạy. Chúng tôi trình bày kết quả về phân tích độ nhạy cấp hai cho bài toán tối ưu đa trị tham số
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More From: Science and Technology Development Journal - Natural Sciences
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