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JGO

2010

2010

We consider a generalized equilibrium problem involving DC functions which is called (GEP). For this problem we establish two new dual formulations based on Toland-Fenchel-Lagrange duality for DC programming problems. The ﬁrst one allows us to obtain a uniﬁed dual analysis for many interesting problems. So, this dual coincides with the dual problem proposed by Martinez-Legaz and Sosa in [23] for equilibrium problems in the sense of Blum and Oettli. Furthermore it is equivalent to Mosco’s dual problem [25] when applied to a variational inequality problem. The second dual problem generalizes to our problem another dual scheme that has been recently introduced by Jacinto and Scheimberg in [18] for convex equilibrium problems. Through these schemes, as by products, we obtain new optimality conditions for (GEP) and also, gap functions for (GEP), which cover the ones in [1, 2] for variational inequalities and standard convex equilibrium problems. These results, in turn, when applied to...

Related Content

Added |
28 Jan 2011 |

Updated |
28 Jan 2011 |

Type |
Journal |

Year |
2010 |

Where |
JGO |

Authors |
N. Dinh, Jean-Jacques Strodiot, Van Hien Nguyen |

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