Order-Preserving Transformations and Applications |
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Authors: | A Cambini DT Luc L Martein |
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Institution: | (1) University of Pisa, Pisa, Italy;(2) University of Avignon, Avignon, France;(3) Institute of Mathematics, Hanoi, Vietnam |
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Abstract: | In this paper, we study the effects of a linear transformation on the partial order relations that are generated by a closed and convex cone in a finite-dimensional space. Sufficient conditions are provided for a transformation preserving a given order. They are applied to derive the relationship between the efficient set of a set and its image under a linear transformation, to characterize generalized convex vector functions by using order-preserving transformations, to establish some calculus rules for the subdifferential of a convex vector function, and develop an optimality condition for a convex vector problem. |
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Keywords: | Partial orders efficient points generalized convex functions subdifferentials |
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