Existence and Lagrangian duality for maximizations of set-valued functions
Journal of Optimization Theory and Applications
An existence theorem in vector optimization
Mathematics of Operations Research
Journal of Optimization Theory and Applications
comparison of existence results for efficient points
Journal of Optimization Theory and Applications
Existence of efficient points in vector optimization and generalized Bishop---Phelps theorem
Journal of Optimization Theory and Applications
Preferred answer sets for ordered logic programs
Theory and Practice of Logic Programming
On solutions of set-valued optimization problems
Computers & Mathematics with Applications
Some equivalent problems in set optimization
Operations Research Letters
Journal of Global Optimization
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In this paper, we study a general optimization problem without linear structure under a reflexive and transitive relation on a nonempty set E, and characterize the existence of efficient points and the domination property for a subset of E through a generalization of the order-completeness condition introduced earlier. Afterwards, we study the abstract optimization problem by using generalized continuity concepts and establish various existence results. As an application, we extend and improve several existence results given in the literature for an optimization problem involving set-valued maps under vector and set criteria.