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Global Optimization from Concave Minimization to Concave Mixed Variational Inequality

icon-email Le Dung Muu , Nguyen Van Quy

Abstract

We use techniques from global optimization to develop an algorithm for finding a global solution of nonconvex mixed variational inequality problems involving separable DC cost functions. In contrast to the convex mixed variational inequality, in these problems, a local solution may not be a global one. The proposed algorithm uses the convex envelope of the separable cost function over boxes to approximate a DC cost problem with a convex cost one that can be solved by available methods. To obtain better approximate solutions, the algorithm uses an adaptive rectangular bisection which is performed only in the space of concave variables. The algorithm is applied to solve the Nash-Cournot and Bertrand equilibrium models with logarithm and quadratic concave costs. Computational results on a lot number of randomly generated data show that the proposed algorithm is efficient for these models, when the number of the concave cost functions is moderate, while the size of the model may be much larger.

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
Messages2TimelineExceptionsViews8RouteQueries108Models432MailsGateSessionRequest
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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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      Metadata
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      Metadata
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