A Fuzzy Based Optimization Model for Nonlinear Programming with Lagrangian Multiplier Conditions

Palanivel K., ÇEBİ S.

Intelligent and Fuzzy Systems - Intelligence and Sustainable Future Proceedings of the INFUS 2023 Conference, İstanbul, Turkey, 22 - 24 August 2023, vol.758 LNNS, pp.440-453 identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 758 LNNS
  • Doi Number: 10.1007/978-3-031-39774-5_50
  • City: İstanbul
  • Country: Turkey
  • Page Numbers: pp.440-453
  • Keywords: Fuzzy nonlinear programming problem, Lagrange’s multiplier conditions with fuzziness, Nonlinear optimization, Trapezoidal fuzzy membership functions
  • Yıldız Technical University Affiliated: Yes


A fuzzy based mathematical model on Lagrangian multiplier conditions has been proposed to address the Non-linear Programming (NLP) with equality constraints. Furthermore, the model demonstrates how multivariable optimization issues can be solved using membership functions. This model is excellent for problem-solving because there is no need to explicitly solve the conditions and utilize them to eliminate additional variables. Then the sufficient conditions for a constrained local maximum or minimum can be stated in terms of a sequence of principal minors of the bordered Hessian matrix of second derivatives of the Lagrangian expression. It also demonstrates how the Lagrange multiplier method can be used for proving the Jacobian matrix. Additionally, the model can be considered in three stages: that is, mathematical formulation, computational procedures, and numerical illustration with comparative analysis. Likewise, the model illustrates the considered problem using two distinct approaches, namely membership functions (MF) and robust ranking index. Finally, the comparison analysis provides detailed results and discussion that justify the optimal outcome in order to address the vagueness of certain NLPPs.