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Generalized Fritz John optimality in nonlinear programming in the presence of equality and inequality constraints

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Abstract

In this paper, we study Fritz John type optimality conditions for constrained nonlinear programming in which equality and inequality constraints are together present. We introduce a generalized Fritz John condition which is necessary and sufficient for a feasible point to be an optimal solution under weak invexity. In particular, by combining the introduced generalized Fritz John condition with the invexity with respect to different functions, we obtain sufficient optimality conditions which extend and generalize various results in the literature, and their importance and usefulness are illustrated on examples .

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Acknowledgments

The authors are grateful to the editor and to the anonymous referees for their valuable suggestions and comments which have helped to improve the quality of this paper.

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Authors and Affiliations

  1. LaMOS Research Unit, Computer Science Department, University of Bejaia, 06000, Bejaia, Algeria

    Hachem Slimani

  2. LaMOS Research Unit, Operational Research Department, University of Bejaia, 06000, Bejaia, Algeria

    Mohammed-Said Radjef

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  1. Hachem Slimani
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  2. Mohammed-Said Radjef
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Correspondence to Hachem Slimani.

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Slimani, H., Radjef, MS. Generalized Fritz John optimality in nonlinear programming in the presence of equality and inequality constraints. Oper Res Int J 16, 349–364 (2016). https://doi.org/10.1007/s12351-015-0206-9

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  • DOI: https://doi.org/10.1007/s12351-015-0206-9

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