Stability of Local Efficiency in Multiobjective Optimization

Stability of Local Efficiency in Multiobjective Optimization 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 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Optimization Theory and Applications Springer Journals

Stability of Local Efficiency in Multiobjective Optimization

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Publisher
Springer US
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operations Research/Decision Theory
ISSN
0022-3239
eISSN
1573-2878
D.O.I.
10.1007/s10957-018-1312-7
Publisher site
See Article on Publisher Site

Abstract

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

Journal of Optimization Theory and ApplicationsSpringer Journals

Published: Jun 4, 2018

References

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