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On Constraint Qualifications for Multiobjective Optimization Problems with Switching Constraints

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Optimization, Variational Analysis and Applications (IFSOVAA 2020)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 355))

Abstract

In this chapter, we consider multiobjective optimization problems with switching constraint (MOPSC). We introduce linear independence constraint qualification (LICQ), Mangasarian–Fromovitz constraint qualification (MFCQ), Abadie constraint qualification (ACQ), and Guignard constraint qualification (GCQ) for multiobjective optimization problems with switching constraint (MOPSC). Further, we introduce the notion of Weak stationarity, Mordukhovich stationarity, and Strong stationarity, i.e., W-stationarity, M-stationarity, and S-stationarity, respectively, for the MOPSC. Also, we present a survey of the literature related to existing constraint qualifications and stationarity conditions for mathematical programs with equilibrium constraints (MPEC), mathematical programs with complementarity constraints (MPCC), mathematical programs with vanishing constraints (MPVC), and for mathematical programs with switching constraints (MPSC). We establish that the M-stationary conditions are sufficient optimality conditions for the MOPSC using generalized convexity. Further, we propose a Wolfe-type dual model for the MOPSC and establish weak duality and strong duality results under assumptions of generalized convexity.

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Acknowledgements

The authors are grateful to anonymous referees for careful reading of the manuscript, which improved the chapter in its present form. We are grateful to Prof. S. K. Mishra for his most valuable support to design this chapter. The second author is supported by the Science and Engineering Research Board, a statutory body of the Department of Science and Technology (DST), Government of India, through project reference no. EMR/2016/002756.

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Authors and Affiliations

  1. Department of Mathematics, Satish Chandra College, Ballia, 277001, India

    Yogendra Pandey

  2. Department of Mathematics, National Institute of Technology, Aizawl, 796012, Mizoram, India

    Vinay Singh

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  1. Yogendra Pandey
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  2. Vinay Singh
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Correspondence to Yogendra Pandey .

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Editors and Affiliations

  1. Institute of Science, Banaras Hindu University, Varanasi, Uttar Pradesh, India

    Vivek Laha

  2. Institut de Mathématiques de Toulouse, Paul Sabatier University, Toulouse, France

    Pierre Maréchal

  3. Institute of Science, Banaras Hindu University, Varanasi, Uttar Pradesh, India

    S. K. Mishra

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Pandey, Y., Singh, V. (2021). On Constraint Qualifications for Multiobjective Optimization Problems with Switching Constraints. In: Laha, V., Maréchal, P., Mishra, S.K. (eds) Optimization, Variational Analysis and Applications. IFSOVAA 2020. Springer Proceedings in Mathematics & Statistics, vol 355. Springer, Singapore. https://doi.org/10.1007/978-981-16-1819-2_13

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