A survey of vector optimization in infinite-dimensional spaces,part 2

The present survey deals with the state of vector optimization as a mathematical discipline. In this context, the optima are generally defined as maximal pointsy₀ with respect to a partial order on the criteria space. The survey is restricted to a discussion of that literature which deals with pointsy₀ which satisfy a maximality condition with respect toy₀-comparable criteria values; papers which are based on a maximality condition satisfied for all admissible criteria values are included only in a supplementary bibliography. For the former, all aspects of the optimization process are surveyed, ranging from questions of existence to the treatment of duality. Particular attention is paid to questions of proper maximality. The discussion is based on a broad range of definitions and selected theorems from the literature.The authors wish to express their appreciation to O. Saleh and Y. H. Liu for their thoughtful ear, their cogent suggestions, and their untiring legwork in procuring and discussing many of the papers cited in this review. Above all, however, their thanks go to Professors L. Hurwicz and J. M. Borwein for the excellent papers they produced in this area. Their work was a pleasure to read, and it provided the supporting framework without which our task would have been a considerably more difficult one.