J Optim Theory Appl https://doi.org/10.1007/s10957-018-1312-7 Stability of Local Efﬁciency in Multiobjective Optimization 1 1 Sanaz Sadeghi · S. Morteza Mirdehghan Received: 4 July 2017 / Accepted: 15 May 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract Analyzing the behavior and stability properties of a local optimum in an optimization problem, when small perturbations are added to the objective functions, are important considerations in optimization. The tilt stability of a local minimum in a scalar optimization problem is a well-studied concept in optimization which is a version of the Lipschitzian stability condition for a local minimum. In this paper, we deﬁne a new concept of stability pertinent to the study of multiobjective optimization problems. We prove that our new concept of stability is equivalent to tilt stability when scalar optimizations are available. We then use our new notions of stability to establish new necessary and sufﬁcient conditions on when strict locally efﬁcient solutions of a multiobjective optimization problem will have small changes when correspondingly small perturbations are added to the objective functions. Keywords Multiobjective programming · Variational analysis · Tilt stability · Weighted sum scalarization Mathematics Subject Classiﬁcation 90C29 · 90C31 · 49K40 Communicated by Fabián
Journal of Optimization Theory and Applications – Springer Journals
Published: Jun 4, 2018
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