Optimization Theory Study

A merit function for variational inequality problem(VIP) was considered in [1] , and it had been generalized in [2]. In this paper , I study the relation between minimizing sequences and stationary sequences of the generalized merit function for variational inequality problem ; In this paper , without the convexity or analyticity assumption , I study error bounds for lower semicontinuous functions in nonned spaces and establish sufficient/necessary conditions on the existence of error bounds in infinite dimensional nonned spaces.