Journal
OPTIMIZATION
Volume 60, Issue 12, Pages 1421-1440Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/02331931003665108
Keywords
vector optimization; solution concept; attainment of infimum; infimal set; lower semicontinuity; Weierstrass existence result
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Over the past decades various solution concepts for vector optimization problems have been established and used: among them are efficient, weakly efficient and properly efficient solutions. In contrast to the classical approach, we define a solution to be a set of efficient solutions on which the infimum of the objective function with respect to an appropriate complete lattice (the space of self-infimal sets) is attained. The set of weakly efficient solutions is not considered to be a solution, but weak efficiency is essential in the construction of the complete lattice. In this way, two classic concepts are involved in a common approach. Several different notions of semicontinuity are compared. Using the space of self-infimal sets, we can show that various originally different concepts coincide. A Weierstrass existence result is proved for our solution concept. A slight relaxation of the solution concept yields a relationship to properly efficient solutions.
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