Unconstrained optimization reformulations of equilibrium problems |
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| Authors: | Li Ping Zhang Ji Ye Han |
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| Affiliation: | (1) Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, P. R. China;(2) Institute of Applied Mathematics, Academy of Mathematics & Systems Science, Chinese Academy of Sciences, Beijing, 100190, P. R. China |
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| Abstract: | We generalize the D-gap function developed in the literature for variational inequalities to a general equilibrium problem
(EP). Through the D-gap function, the equilibrium problem is cast as an unconstrained minimization problem. We give conditions
under which any stationary point of the D-gap function is a solution of EP and conditions under which it provides a global
error bound for EP. Finally, these results are applied to box-constrained EP and then weaker conditions are established to
obtain the desired results for box-constrained EP.
This work is partly supported by the National Natural Science Foundation of China (Grant No. 10871113, 10671013) |
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| Keywords: | equilibrium problems D-gap function error bound unconstrained optimization |
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