Enhanced Efficiency in Multi-objective Optimization

Y. Jiang and S. Deng ()
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Y. Jiang: Nanjing University of Information Science and Technology
S. Deng: Northern Illinois University

Journal of Optimization Theory and Applications, 2014, vol. 162, issue 2, No 13, 577-588

Abstract: Abstract For a given multi-objective optimization problem, we introduce and study the notion of α-proper efficiency. We give two characterizations of such proper efficiency: one is in terms of exact penalization and the other is in terms of stability of associated parametric problems. Applying the aforementioned characterizations and recent results on global error bounds for inequality systems, we obtain verifiable conditions for α-proper efficiency. For a large class of polynomial multi-objective optimization problems, we show that any efficient solution is α-properly efficient under some mild conditions. For a convex quadratically constrained multi-objective optimization problem with convex quadratic objective functions, we show that any efficient solution is α-properly efficient with a known estimate on α whenever its constraint set is bounded. Finally, we illustrate our achieved results with examples, and give an example to show that such an enhanced efficiency property may not hold for multi-objective optimization problems involving C ∞-functions as objective functions.

Keywords: Efficient solution; Properly efficient solution; α-properly efficient solution; Exact penalization; Polynomial multi-objective optimization; Global error bound (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10957-013-0486-2

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