An external penalty-type method for multicriteria

We propose an extension of the classical real-valued external penalty method to the multicriteria optimization setting. As its single objective counterpart, it also requires an external penalty function for the constraint set, as well as an exogenous divergent sequence of nonnegative real numbers, t...

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Bibliographic Details
Published inTOP Vol. 24; no. 2; pp. 493 - 513
Main Authors Fukuda, Ellen H., Drummond, L. M. Graña, Raupp, Fernanda M. P.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2016
Subjects
Business and Management
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Finance
Industrial and Production Engineering
Insurance
Management
Operations Research/Decision Theory
Optimization
Original Paper
Statistics for Business
Constrained multiobjective optimization
Pareto optimality
90C29
90C30
External penalty method
Scalar representation
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Summary:We propose an extension of the classical real-valued external penalty method to the multicriteria optimization setting. As its single objective counterpart, it also requires an external penalty function for the constraint set, as well as an exogenous divergent sequence of nonnegative real numbers, the so-called penalty parameters, but, differently from the scalar procedure, the vector-valued method uses an auxiliary function, which can be chosen among large classes of “monotonic” real-valued mappings. We analyze the properties of the auxiliary functions in those classes and exhibit some examples. The convergence results are similar to those of the scalar-valued method, and depending on the kind of auxiliary function used in the implementation, under standard assumptions, the generated infeasible sequences converge to weak Pareto or Pareto optimal points. We also propose an implementable local version of the external penalization method and study its convergence results.
ISSN:1134-5764
1863-8279
DOI:10.1007/s11750-015-0406-8