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DUALITY FOR RADIANT AND SHADY PROGRAMS

J.-P. PENOT

Abstract

We consider the two classes of closed convex sets which are stable under dilatations and shrinkings respectively (homotheties of rates greater than one and less than one respectively). We define conjugacies for the classes of functions whose sublevel sets belong to these classes. For such functions, the conjugate can be defined on the dual space and an extra parameter is not needed. We apply these notions to the maximization of a convex function on a convex set and to the minimization of a convex function on the set of points outside a convex subset. We introduce several dual problems related to each of these problems and we give conditions
ensuring there is no duality gap.

Viện Toán học, Viện Hàn lâm Khoa học và Công nghệ Việt Nam

Địa chỉ: Số 18 đường Hoàng Quốc Việt, quận Cầu Giấy, Hà Nội

Điện thoại: 024 37563474 - Fax: 024 37564303

Email: vientoan@math.ac.vn

Viện nghiên cứu cao cấp về toán Hội Toán học Mỹ MathScinet Thư viện số (VAST) Arxiv
Lịch hoạt động chung Lịch sử dụng phòng, hội trường, hội thảo Ảnh hoạt động
Giới thiệu Đăng nhập Đăng ký tài khoản Quên mật khẩu Chính sách bảo mật
Messages2TimelineExceptionsViews8RouteQueries108Models431MailsGateSessionRequest
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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