Free Disposal Hull Condition to Verify When Efficiency Coincides with Weak Efficiency

Naoki Hamada () and Shunsuke Ichiki ()
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Naoki Hamada: KLab Inc.
Shunsuke Ichiki: Tokyo Institute of Technology

Journal of Optimization Theory and Applications, 2022, vol. 192, issue 1, No 10, 248-270

Abstract: Abstract In solving a multi-objective optimization problem by scalarization techniques, solutions to a scalarized problem are, in general, weakly efficient rather than efficient to the original problem. Thus, it is crucial to understand what condition ensures that all weakly efficient solutions are efficient. In this paper, we give a condition to verify when efficiency coincides with weak efficiency, provided that the free disposal hull of a given set is convex. By using this characterization, we obtain various applications to multi-objective optimization problems under some convex conditions. We also apply the main theorem to the least absolute shrinkage and selection operator (LASSO) and show that for a multi-objective version of LASSO, all weakly efficient solutions are efficient. Numerical simulation demonstrates that this equivalence is helpful to accelerate the hyper-parameter search for LASSO.

Keywords: Multi-objective optimization; Free disposal hull; Weak efficiency; Efficiency; Sparse modeling; 90C25; 90C29 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10957-021-01961-5

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