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The Lipschitz Properties of the Value Function and the Solution Map to a Parametric Discrete Optimal Control Problem

icon-email Nguyen Thi Toan , Le Quang Thuy

Abstract

Motivated by the works of Toan and Kien (J. Nonlinear Convex Anal.12:635–650, 2011) and Thuy and Toan (Acta Math. Vietnam.43:175–199, 2018) on the stability and the solution sensitivity in parametric discrete optimal control problems, this paper is devoted to the study of the Lipschitz property of the value function and the Aubin property of the solution map to a parametric dynamic programming problem with linear constraints. By establishing abstract results on the Lipschitz property of the value function to a parametric programming and the Aubin property of the solution map to a parametric variational inequality, we obtain the Lipschitz property of the value function and the Aubin property of the solution map to a parametric discrete optimal control problem.

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
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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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      Metadata
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      Metadata
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      Metadata
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      Metadata
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