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In this study, some new order relations on family of sets are introduced by using Minkowski difference. The relations between these orders and the ordering cone of the vector space are obtained. It is shown that depending on the corresponding cone, these order relations are partial orders on the family of nonempty bounded sets. Some relationships between these order relations and upper and lower set less order relations are investigated. Also, two scalarizing functions are introduced in order to replace set optimization problems with respect to these partial order relations with scalar optimization problems. Moreover, necessary and sufficient optimality conditions are presented. [ABSTRACT FROM AUTHOR]

In this work, it is proved that weak exhausters of a positively homogeneous function can be reduced if weak subdifferential/superdifferential can be represented as the sum of a subset of it and weak subdifferential of zero function. It is also shown that weak exhausters can be reduced if this subset is the set of minimal elements of weak subdifferential/superdifferential with respect to weak subdifferential of zero function. At the end, some optimality conditions are given using reduced weak exhausters. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a construction method of total ordering cone on $${\mathbb{R}^n}$$ . It is shown that any total ordering cone on $${\mathbb{R}^n}$$ is isomorphic to the cone $${\mathbb{R}^n_{lex}}$$ . Existence of a total ordering cone that contain given cone with a compact base is shown. By using this cone, a solving method of vector and set valued optimization problems is presented. [ABSTRACT FROM AUTHOR]