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Zbl 1163.58305
He, Bingsheng; He, Xiao-Zheng; Liu, Henry X.; Wu, Ting
Self-adaptive projection method for co-coercive variational inequalities. (English)
[J] Eur. J. Oper. Res. 196, No. 1, 43-48 (2009). ISSN 0377-2217

Summary: In some real-world problems, the mapping of the variational inequalities does not have any explicit forms and only the function value can be evaluated or observed for given variables. In this case, if the mapping is co-coercive, the basic projection method is applicable. However, in order to determine the step size, the existing basic projection method needs to know the co-coercive modulus in advance. In practice, usually even if the mapping can be characterized co-coercive, it is difficult to evaluate the modulus, and a conservative estimation will lead an extremely slow convergence. In view of this point, this paper presents a self-adaptive projection method without knowing the co-coercive modulus. We also give a real-life example to demonstrate the practicability of the proposed method.

MSC 2000:: *58J35 Heat and other parabolic equation methods
49J40 Variational methods including variational inequalities

Keywords: convex programming; co-coercive; projection method; variational inequalities

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