Please use this identifier to cite or link to this item: https://dspace.ctu.edu.vn/jspui/handle/123456789/100870
Title: Global optimization from concave minimization to concave mixed variational inequality
Authors: Le, Dung Muu
Nguyen, Van Quy
Keywords: DC optimization
Nonconvex mixed variational inequality
Nash cournot oligopolistic model
Concave cost
Global solution
Gap function
Convex envelope
Issue Date: 2020
Series/Report no.: Acta mathematica Vietnamica journal;Vol.45, No.02 .- P.449-462
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.
URI: https://dspace.ctu.edu.vn/jspui/handle/123456789/100870
ISSN: 0251-4184
Appears in Collections:Acta Mathematica Vietnamica 

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