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Volume 1, Issue 1, 1 April 2019, Pages 13-24
Abstract. We consider the Nash-Cournot oligopolistic equilibrium models involving separable concave cost functions. In contrast to the models with linear and convex cost functions, a local equilibrium point may not be a global one in the models. We propose two algorithms for finding global and local equilibrium points of the models having separable concave cost functions by using a DC decomposition of a gap function. The first algorithm uses the convex envelope of a separable concave cost function to approximate a concave cost model with affine cost ones. The latter is equivalent to strongly convex quadratic programs that can be solved efficiently. To obtain better approximate solutions, the first algorithm uses an adaptive rectangular bisection which is performed only in the space of concave variables. The second algorithm is an extension of the proximal method to the models.
How to Cite this Article:
Le Dung Muu, Nguyen Van Quy, DC-gap function and proximal methods for solving Nash-Cournot oligopolistic equilibrium models involving concave cost, J. Appl. Numer. Optim. 1 (2019), 13-24.