Duality for <Emphasis Type="Italic">ε</Emphasis>-Variational Inequality |
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Authors: | S Kum G S Kim G M Lee |
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Institution: | (1) Department of Mathematics Education, Chungbuk National University, Cheongju, 361-763, Korea;(2) Department of Applied Mathematics, Pukyong National University, Pusan, 608-737, Korea |
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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.
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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Keywords: | ε -Variational inequality Dual problems Fenchel duality ε -Optimal solutions |
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