Necessary optimality conditions and saddle points for approximate optimization in banach spaces

In this article we study approximate optimality in the setting of a Banach space. We study various solution concepts existing in the literature and develop very general necessary optimality conditions in terms of limiting subdifferentials. We also study saddle point conditions and relate them to various solution concepts. Part of this research was carried out when the author was a post-doctoral fellow at UAB, Barcelona by the Grant No. SB99-B0771103B of the Spanish Ministry of Education and Culture. The hospitality and the facilities provided at CODE, UAB is gratefully acknowledged.