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Proper Efficiency and Proper Karush–Kuhn–Tucker Conditions for Smooth Multiobjective Optimization Problems

Abstract

Proper Karush–Kuhn–Tucker (PKKT) conditions are said to hold when all the multipliers of the objective functions are positive. In 2012, Burachik and Rizvi introduced a new regularity condition under which PKKT conditions hold at every Geoffrion-properly efficient point. In general, the set of Borwein properly-efficient points is larger than the set of Geoffrion-properly efficient points. Our aim is to extend the PKKT conditions to the larger set of Borwein-properly efficient points.

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Acknowledgements

We are thankful to Jonathan M. Borwein, for pointing out to us that the results in [9] only need local proper efficiency, such as the one introduced by him in [7].

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Correspondence to Regina S. Burachik.

Additional information

M.M. Rizvi was supported by UniSA President’s Scholarships and the School of Information Technology and Mathematical Sciences at University of South Australia.

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Burachik, R.S., Rizvi, M.M. Proper Efficiency and Proper Karush–Kuhn–Tucker Conditions for Smooth Multiobjective Optimization Problems. Vietnam J. Math. 42, 521–531 (2014). https://doi.org/10.1007/s10013-014-0102-2

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  • DOI: https://doi.org/10.1007/s10013-014-0102-2

Keywords

  • Multiobjective optimization
  • Regularity conditions
  • Optimality conditions for efficient solutions
  • Geoffrion-properly efficient solutions
  • Borwein-properly efficient solutions
  • Proper Karush–Kuhn–Tucker conditions

Mathematics Subject Classification (2010)

  • 90C29