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On weak conjugacy, augmented Lagrangians and duality in nonconvex optimization

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Abstract

In this paper, zero duality gap conditions in nonconvex optimization are investigated. It is considered that dual problems can be constructed with respect to the weak conjugate functions, and/or directly by using an augmented Lagrangian formulation. Both of these approaches and the related strong duality theorems are studied and compared in this paper. By using the weak conjugate functions approach, special cases related to the optimization problems with equality and inequality constraints are studied and the zero duality gap conditions in terms of objective and constraint functions, are established. Illustrative examples are provided.

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Acknowledgements

The authors would like to thank the associate editor and the reviewers for all of their careful, constructive and insightful comments and suggestions, which have been very helpful in improving the manuscript.

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  1. Department of Industrial Engineering, Faculty of Engineering, Eskisehir Technical University, Iki Eylul Campus, 26555, Eskisehir, Turkey

    Gulcin Dinc Yalcin & Refail Kasimbeyli

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  1. Gulcin Dinc Yalcin
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  2. Refail Kasimbeyli
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Correspondence to Refail Kasimbeyli.

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Yalcin, G.D., Kasimbeyli, R. On weak conjugacy, augmented Lagrangians and duality in nonconvex optimization. Math Meth Oper Res 92, 199–228 (2020). https://doi.org/10.1007/s00186-020-00708-8

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  • DOI: https://doi.org/10.1007/s00186-020-00708-8

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