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Bazaraa, M.S., Sherali, H.D. and Shetty, C.M. (1993) Nonlinear Programming. 2nd Edition, John Wiley and Sons, New York.

has been cited by the following article:

• TITLE: Guignard’s Constraint Qualification (GCQ) and Multiobjective Optimisation Problems

  AUTHORS: H. S. Faruque Alam, Ganesh Chandra Ray

  KEYWORDS: Constraint Qualifications, Multiobjective Optimization, Karush Kuhn-Tucker Conditions, Constraint Optimization

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.10 No.7, July 29, 2022

  ABSTRACT: Investigation of optimality conditions has been one of the most interesting topics in the theory of multiobjective optimisation problems (MOP). To derive necessary optimality conditions of MOP, we consider assumptions called constraints qualifications. It is recognised that Guignard Constraint Qualification (GCQ) is the most efficient and general assumption for scalar objective optimisation problems; however, GCQ does not ensure Karush-Kuhn Tucker (KKT) necessary conditions for multiobjective optimisation problems. In this paper, we investigate the reasons behind that GCQ are not allowed to derive KKT conditions in multiobjective optimisation problems. Furthermore, we propose additional assumptions that allow one to use GCQ to derive necessary conditions for multiobjective optimisation problems. Finally, we also include sufficient conditions for multiobjective optimisation problems.