Volume 49, Number 5, December 2015
|Page(s)||845 - 864|
|Published online||19 February 2016|
A jointly constrained bilinear programming method for solving generalized Cournot–Pareto models∗
Academy of Finance, Hanoi, Vietnam
Received: 1 February 2015
Accepted: 8 August 2015
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.
Mathematics Subject Classification: 47J20 / 49J40
Key words: Generalized Cournot model / bilinear programming / branch-and-bound / Pareto solution
© EDP Sciences, ROADEF, SMAI 2016
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