LP-Well-posedness Of Several Classes Of Constrained Variational Inequalities Problems

Tykhonov-well-posedness and LP-well-posedness play a central role in the study of Optimization Problems and Variational Inequality Problems, particularly in their algorithms and algorithms convergence. Researching in well-posedness and LP-well-posedness is one of the important aspects in Optimization Theory. In this paper, we mainly investigate three classes of constrained variational inequality problems. First, we recall the results obtained in [15] and [49], Huang have given the definitions of LP-well-posedness ,and this paper have the definitions of the LP-well-posedness for usual constrained Variational Inequality Problems(VIP) and discuss the conditions which the LP-well-posedness of (VIP) holds. From reference [50], We define four types LP-well-posedness in constrained Generalized Variational Inequality Problems(GVIP). relationship of the four types LP-well-posedness are presented, and we have some sufficient conditions and necessary conditions which the (GVIP) LP-well-posedness holds.In the last Chapter, The study of LP-well-posedness is extended to the Quasi-Variational Inequality Problems(QVIP). We define four types of Lp-well-posedness in constrained Quasi-Variational Inequality Problems.Some criteria and characterizations for there types of LP-well-posedness are derived. Their relationships are presented. Specially, when the set-valued mapping S is low-semicontinuous and closed, the operator A is continuous ,we discuss the (Generalized) I type LP-well-posedess, and we have some results.