Lê Thanh Tùng * , Trần Thiện Khải , Phạm Thanh Hùng Phạm Lê Bạch Ngọc

* Tác giả liên hệ (lttung@ctu.edu.vn)

Abstract

The paper deals with the necessary and sufficient optimality conditions for the convex optimization problem with  convex feasible set defined by infinite inequality constraints in the both cases, smooth and nonsmooth data. The results enhance some recent KKT type theorems by Lasserre for differentiable functions and by Dutta and Lalitha for Lipschitz functions.
Keywords: Semi-infinite programming, Michel-Penot subdifferential, optimality conditions, convex optimization, smooth and nonsmooth optimization

Tóm tắt

Bài báo này khảo sát điều kiện tối ưu cần và đủ cho bài toán tối ưu lồi có tập chấp nhận được lồi được định nghĩa bởi vô hạn ràng buộc bất đẳng thức cả trong trường hợp trơn và không trơn. Kết quả đã phát triển một số định lý điều kiện tối ưu dạng KKT gần đây bởi Lasserre đối với lớp hàm khả vi và bởi Dutta và Lalitha đối với lớp hàm Lipschitz.
Từ khóa: Bài toán tối ưu nửa vô hạn, dưới vi phân Michel-Penot, điều kiện tối ưu, tối ưu lồi, tối ưu trơn và không trơn

Article Details

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