Journal of Global Optimization

, Volume 70, Issue 4, pp 903–916

# Scalarizations for a unified vector optimization problem based on order representing and order preserving properties

• Khushboo
• C. S. Lalitha
Article

## Abstract

The aim of this paper is to study characterizations of minimal and approximate minimal solutions for a unified vector optimization problem in a Hausdorff real topological vector space. These characterizations have been obtained via scalarizations which are based on general order representing and order preserving properties. A nonlinear scalarization based on Gerstewitz function is shown to be a particular case of the proposed scalarizations. Furthermore, in the setting of normed space, characterizations are given for minimal solutions by using scalarization function based on the oriented distance function. Finally, under appropriate assumptions it is shown that this function satisfies order representing and order preserving properties.

## Keywords

Nonlinear scalarization Order representing property Order preserving property Gerstewitz function Oriented distance function

## Mathematics Subject Classification

90C26 90C29 90C46

## Notes

### Acknowledgements

The authors are thankful to the anonymous referee for the valuable suggestions which improved the quality of the paper. Research of C.S. Lalitha is supported by R&D Research Development Grant to University Faculty, University of Delhi.

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