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Duality for ε-Variational Inequality

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Abstract

In this paper, following the method in the proof of the composition duality principle due to Robinson and using some basic properties of the ε-subdifferential and the conjugate function of a convex function, we establish duality results for an ε-variational inequality problem. Then, we give Fenchel duality results for the ε-optimal solution of an unconstrained convex optimization problem. Moreover, we present an example to illustrate our Fenchel duality results for the ε-optimal solutions.

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Authors and Affiliations

  1. Department of Mathematics Education, Chungbuk National University, Cheongju, 361-763, Korea

    S. Kum

  2. Department of Applied Mathematics, Pukyong National University, Pusan, 608-737, Korea

    G. S. Kim & G. M. Lee

Authors
  1. S. Kum
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  2. G. S. Kim
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  3. G. M. Lee
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Corresponding author

Correspondence to G. M. Lee.

Additional information

Communicated by X.Q. Yang.

The authors thank the referees for valuable suggestions and comments. This work was supported by Grant No. R01-2003-000-10825-0 from the Basic Research Program of KOSEF.

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Kum, S., Kim, G.S. & Lee, G.M. Duality for ε-Variational Inequality. J Optim Theory Appl 139, 649–655 (2008). https://doi.org/10.1007/s10957-008-9403-5

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  • DOI: https://doi.org/10.1007/s10957-008-9403-5

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