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Mathematical analysis of desirability functions.

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Τίτλος: Mathematical analysis of desirability functions.
Συγγραφείς: Akteke-Öztürk, Başak1,2,3 (AUTHOR) bozturk@metu.edu.tr, Weber, Gerhard Wilhelm1,2,3 (AUTHOR), Köksal, Gülser1,2,3 (AUTHOR)
Πηγή: Central European Journal of Operations Research. Sep2026, Vol. 34 Issue 3, p987-999. 13p.
Θεματικοί όροι: *Mathematical analysis, Lipschitz continuity, Optimization algorithms, Smoothness of functions, Multi-objective optimization
Περίληψη: In this study, we present the different aspects of functional properties of desirability functions which is a scalarization method for multi-response optimization problems (MROPs). In a multiple-response optimization problem, the aim is to define and achieve the optimal conditions for a process, product or system by considering multiple response variables simultaneously. Desirability functions is currently a well-known and powerful tool for researchers and scientist who study MROPS. The paper presents a study on the mathematical analysis of desirability functions focusing on two key aspects: Lipschitz continuity and Clarke generalized derivative. The paper highlights the importance of understanding the mathematical properties of desirability functions in decision-making and optimization. The findings of the paper have implications for the development of optimization algorithms and strategies for handling nonsmooth functions. We end with a conclusion and an outlook to future researches and applications. [ABSTRACT FROM AUTHOR]
Copyright of Central European Journal of Operations Research is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  – Url: https://dx.doi.org/doi:10.1007/s10100-025-00990-z
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  Data: In this study, we present the different aspects of functional properties of desirability functions which is a scalarization method for multi-response optimization problems (MROPs). In a multiple-response optimization problem, the aim is to define and achieve the optimal conditions for a process, product or system by considering multiple response variables simultaneously. Desirability functions is currently a well-known and powerful tool for researchers and scientist who study MROPS. The paper presents a study on the mathematical analysis of desirability functions focusing on two key aspects: Lipschitz continuity and Clarke generalized derivative. The paper highlights the importance of understanding the mathematical properties of desirability functions in decision-making and optimization. The findings of the paper have implications for the development of optimization algorithms and strategies for handling nonsmooth functions. We end with a conclusion and an outlook to future researches and applications. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Central European Journal of Operations Research is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s10100-025-00990-z
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      – Code: eng
        Text: English
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        PageCount: 13
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        Type: general
      – SubjectFull: Lipschitz continuity
        Type: general
      – SubjectFull: Optimization algorithms
        Type: general
      – SubjectFull: Smoothness of functions
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              M: 09
              Text: Sep2026
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              Y: 2026
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