Generalized Error Bound For Conic Inequality In （?）~2 Type Banach Spaces

Sensitivity analysis of mathematical programming and convergence analysis of some algorithms of optimization problems,which are quite interesting topics,are deeply tied to the notion of error bound and H（?）lder error bound.Ioffe first characterized error bound in terms of the subdifferentials in his seminal work.Recently,Zheng and Ng extended Ioffe’s classic result to the conic inequality case in Asplund spaces in terms of the conic subdifferential?KΦdefined by the Fr（?）chet normal cone.Furthermore,Yao and Zheng considered H（?）lder error bound and also extended error bound to the generalized error bound.In the thesis,we consider generalized error bound issues for conic inequalities in （?）~2type Banach Spaces.Using the techniques of variational analysis and in terms of proximal subdifferenetials of vector-valued functions,we provide sufficient conditions for the existence of a generalized error bound for a conic inequality.We provide a sharp-er result and give a relationship between the modulus of error bound and corresponding radius with（?）_KΦ（x）replaced by（?）_K^PΦ（x）.In particular,our results improve and extend some existing results.