Generalized Gap Functions and Error Bounds for Generalized Variational Inequalities
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摘要: 针对两类广义变分不等式，分别定义了几族广义间隙函数，并研究其性质．利用这些广义间隙函数，在所研究变分不等式问题的目标函数F关于解是g-强单调的条件下,得到了误差界估计，这里不需要假设F是连续可微或局部Lipschitz的．Abstract: Some classes of generalized gap functions for two kinds of generalized variational inequality problems are considered. Error bounds for the underlying variational inequalities by using the generalized gap functions under the condition that the involved mapping F is gstrongly monotone with respect to the solution were obtained. It is not necessary to suppcsethat Fis continuously differential nor of local Lipschitz. with respect to the solution were obtained. It is not necessary to suppose that Fis continuously differentiable local Lipschitz.
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Key words:
- variational inequality /
- gap functions /
- error bounds
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[1] Fukushima M. Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems[J].Mathematical Programming,1992,53(1):99-110. doi: 10.1007/BF01585696 [2] Wu J H,Florian M,Marcotte P.A general descent framework for the monotone variational inequality problem[J].Mathematical Programming,1993,61(3):281-300. doi: 10.1007/BF01582152 [3] Yamashita N,Taji K,Fukushima M.Unconstrained optimization reformulations of variational inequality problems[J].Journal of Optimization Theory and Applications,1997,92(3):439-456. doi: 10.1023/A:1022660704427 [4] Huang L R,Ng K F. Equivalent optimization formulations and error bounds for variational inequality problem[J].Journal of Optimization Theory and Applications,2005,125(2):299-314. doi: 10.1007/s10957-004-1839-7 [5] Tan L L. Regularized gap functions for nonsmooth variational inequality problems[J].Journal of Mathematical Analysis and Applications,2007,334(2):1022-1038. doi: 10.1016/j.jmaa.2007.01.025 [6] Solodov M V.Merit functions and error bounds for generalized variational inequalities[J].Journal of Mathematical Analysis and Applications,2003,287(2):405-414. doi: 10.1016/S0022-247X(02)00554-1 [7] Noor M A. Merit functions for general variational inequalities[J].Journal of Mathematical Analysis and Applications,2006,316(2):736-752. doi: 10.1016/j.jmaa.2005.05.011 [8] Qu B, Wang C Y,Zhang J Z. Convergence and error bound of a method for solving variational inequality problems via the generalized D-gap function[J].Journal of Optimization Theory and Applications,2003,119(3):535-552. doi: 10.1023/B:JOTA.0000006688.13248.04 -
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