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Second order monotonicities and second order variational-like inequality problems

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Abstract

The purpose of this paper is to introduce the concept of generalized second order invex monotonicities and investigate the relations between generalized second order invex functions with the generalized second order invex monotonicities of their gradient functions. We also introduce the notion of second order variational-like inequality problem and explore the conditions for existence and uniqueness of their solutions. Furthermore, we relate the solution of a mathematical programming problem involving second order invex function with the solution of second order variational-like inequality problem. Also, we provide examples to verify our results.

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Acknowledgments

The research of the second author is financially supported by SERB-DST, New Delhi, India through Grant No. SR/FTP/MS-007/2011. The authors are greatly indebted to the reviewer for her/his valuable comments and suggestions leading to revised version of the original draft for this paper.

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Authors and Affiliations

  1. Department of Applied Mathematics, Indian School of Mines, Dhanbad, Jharkhand, 826004, India

    Sarita Choudhury & Anurag Jayswal

  2. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    I. Ahmad

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  1. Sarita Choudhury
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  2. Anurag Jayswal
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  3. I. Ahmad
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Correspondence to Sarita Choudhury.

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Choudhury, S., Jayswal, A. & Ahmad, I. Second order monotonicities and second order variational-like inequality problems. Rend. Circ. Mat. Palermo 65, 123–137 (2016). https://doi.org/10.1007/s12215-015-0224-8

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  • DOI: https://doi.org/10.1007/s12215-015-0224-8

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