Mathematical analysis of desirability functions

ÖZTÜRK B., Weber G. W., Köksal G.

Central European Journal of Operations Research, 2025 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Publication Date: 2025
  • Doi Number: 10.1007/s10100-025-00990-z
  • Journal Name: Central European Journal of Operations Research
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, IBZ Online, ABI/INFORM, Business Source Elite, Business Source Premier, EconLit, zbMATH, Civil Engineering Abstracts
  • Keywords: Desirability functions, Lipschitz constant, Lipschitz continuity, Multi-objective optimization, Multi-response optimization, Nonsmooth optimization, Operations research
  • TED University Affiliated: Yes

Abstract

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.