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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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