Order-Preserving Transformations and Applications

A. Cambini, D.T. Luc and L. Martein
Additional contact information
A. Cambini: University of Pisa
D.T. Luc: University of Avignon
L. Martein: University of Pisa

Journal of Optimization Theory and Applications, 2003, vol. 118, issue 2, No 4, 275-293

Abstract: 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.

Keywords: Partial orders; efficient points; generalized convex functions; subdifferentials (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (3)

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DOI: 10.1023/A:1025495204834

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