Stability of Local Efficiency in Multiobjective Optimization
| Autor: | S. Morteza Mirdehghan, Sanaz Sadeghi |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Mathematical optimization
021103 operations research Control and Optimization Optimization problem Applied Mathematics 0211 other engineering and technologies Scalar (physics) Stability (learning theory) 02 engineering and technology Management Science and Operations Research Multi-objective optimization Scalar optimization Local optimum Theory of computation 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing Variational analysis Mathematics |
| Zdroj: | Journal of Optimization Theory and Applications. 178:591-613 |
| ISSN: | 1573-2878 0022-3239 |
| DOI: | 10.1007/s10957-018-1312-7 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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