Upper robust mappings and vector minimization: An integral approach

A study of upper robust mapping from a topological space to Rⁿ and development of optimality conditions for vector minimization of upper robust mappings are presented in the framework of integral based optimization theory. Under some general assumptions, optimality conditions are established for several well developed scalarization techniques such as weighting, ϵ-constraint and reference point. These optimality conditions are applied to design integral algorithms for finding the set of efficient solutions of a vector optimization problem. A numerical example is presented to illustrate the effectiveness of the algorithm.