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Optimality conditions and duality theorems for nonsmooth semi-infinite interval-valued mathematical programs with vanishing constraints

Van Su Department of Mathematics, The University of Danang-University of Science and Education, 459 Ton Duc Thang, Lien Chieu, Da Nang, Viet Nam|
Dinh Dieu (55931283100) |

Computational and Applied Mathematics Số 8, năm 2022 (Tập 41, trang -)

ISSN: 22383603

ISSN: 22383603

DOI: 10.1007/s40314-022-02139-z

Tài liệu thuộc danh mục:



Từ khóa: Functions; Mathematical programming; Optimal systems; (VC-) KKT type optimality condition; Dual model; Hadamard; Interval-valued; Locally LU optimal solution; Mathematical programming problem; Nonsmooth semi-infinite interval-valued mathematical programming problem with vanishing constraint; Optimal solutions; Optimality conditions; Semi-infinite intervals; Upper and low hadamard derivative; Wolfe and mond–weir type dual model; Weirs
Tóm tắt tiếng anh
(VC-) Karush–Kuhn–Tucker type necessary and sufficient optimality conditions for locally (weakly) LU optimal solutions in terms of upper and lower Hadamard derivatives with the class of pseudo-convex functions are established for the nonsmooth semi-infinite interval-valued mathematical programming problem with vanishing constraints. We first derive Karush–Kuhn–Tucker-type necessary optimality conditions for such a problem. We second provide sufficient optimality conditions under suitable assumptions on the pseudo-convexity of objective and constraint functions for that problem. Besides, some stationary conditions are also proposed for this problem according to the hypotheses of the Abadie constraint qualifications. Based on these necessary and sufficient optimality conditions, we construct a Wolfe and Mond–Weir types dual problem for such problem in terms of Hadamard derivatives and then establish some weak, strong and converse duality theorems for the same under suitable assumptions on the pseudo-convexity at the point under consideration. Several examples are also provided for the main results of the paper. © 2022, The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional.

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