Geodesic
A jointly constrained bilinear programming method for solving generalized Cournot–Pareto models
Van Quy, Nguyen1
1 Academy of Finance, Hanoi, Vietnam
RAIRO - Operations Research - Recherche Opérationnelle, Tome 49 (2015) no. 5, pp. 845-864

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We propose a vector optimization approach to linear Cournot oligopolistic market equilibrium models where the strategy sets depend on each other. We use scalarization technique to find a Pareto efficient solution to the model by using a jointly constrained bilinear programming formulation. We then propose a decomposition branch-and-bound algorithm for globally solving the resulting bilinear problem. The subdivision takes place in one-dimensional intervals that enables solving the problem with relatively large sizes. Numerical experiments and results on randomly generated data show the efficiency of the proposed algorithm.

DOI : 10.1051/ro/2015031
Classification : 47J20, 49J40
Keywords: Generalized Cournot model, bilinear programming, branch-and-bound, Pareto solution

Van Quy, Nguyen 1

1 Academy of Finance, Hanoi, Vietnam 
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     title = {A jointly constrained bilinear programming method for solving generalized {Cournot{\textendash}Pareto} models},
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Van Quy, Nguyen. A jointly constrained bilinear programming method for solving generalized Cournot–Pareto models. RAIRO - Operations Research - Recherche Opérationnelle, Tome 49 (2015) no. 5, pp. 845-864. doi: 10.1051/ro/2015031

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