A barrier-type method for multiobjective optimization

For solving constrained multicriteria problems, we introduce the multiobjective barrier method (MBM), which extends the scalar-valued internal penalty method. This multiobjective version of the classical method also requires a penalty barrier for the feasible set and a sequence of nonnegative penalt...

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Bibliographic Details
Published inOptimization Vol. 69; no. 11; pp. 2471 - 2487
Main Authors Fukuda, Ellen H., Drummond, L. M. Graña, Raupp, Fernanda M. P.
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 01.11.2020
Taylor & Francis LLC
Subjects
Barrier methods
Continuity (mathematics)
Convergence
multiobjective optimization
Multiple criterion
Multiple objective analysis
Pareto optimality
Pareto optimization
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Summary:For solving constrained multicriteria problems, we introduce the multiobjective barrier method (MBM), which extends the scalar-valued internal penalty method. This multiobjective version of the classical method also requires a penalty barrier for the feasible set and a sequence of nonnegative penalty parameters. Differently from the single-valued procedure, MBM is implemented by means of an auxiliary 'monotonic' real-valued mapping, which may be chosen in a quite large set of functions. Here, we consider problems with continuous objective functions, where the feasible sets are defined by finitely many continuous inequalities. Under mild assumptions, and depending on the monotonicity type of the auxiliary function, we establish convergence to Pareto or weak Pareto optima. Finally, we also propose an implementable version of MBM for seeking local optima and analyse its convergence to Pareto or weak Pareto solutions.
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2019.1576667