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World Congress on Global Optimization

WCGO 2019: Optimization of Complex Systems: Theory, Models, Algorithms and Applications pp 660–671Cite as

On the Applications of Nonsmooth Vector Optimization Problems to Solve Generalized Vector Variational Inequalities Using Convexificators

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 991))

Abstract

In this paper, we employ the characterization for an approximate convex function in terms of its convexificator to establish the relationships between the solutions of Stampacchia type vector variational inequality problems in terms of convexificator and quasi efficient solution of a nonsmooth vector optimization problems involving locally Lipschitz functions. We identify the vector critical points, the weak quasi efficient points and the solutions of the weak vector variational inequality problem under generalized approximate convexity assumptions. The results of the paper extend, unify and sharpen corresponding results in the literature. In particular, this work extends and generalizes earlier works by Giannessi [11], Upadhyay et al. [31], Osuna-Gomez et al. [30], to a wider class of functions, namely the nonsmooth approximate convex functions and its generalizations. Moreover, this work sharpens earlier work by Daniilidis and Georgiev [5] and Mishra and Upadhyay [23], to a more general class of subdifferentials known as convexificators.

The first author is supported by the Science and Engineering Research Board (SERB), Department of Science and Technology, India under Early Career Reasearch (ECR) advancement scheme through grant no. ECR/2016/001961.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Patna, Patna, 801106, India

    Balendu Bhooshan Upadhyay & Priyanka Mishra

  2. University of Central Florida, Orlando, FL, 32816, USA

    Ram N. Mohapatra

  3. Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, 221005, India

    Shashi Kant Mishra

Authors
  1. Balendu Bhooshan Upadhyay
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  2. Priyanka Mishra
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  3. Ram N. Mohapatra
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  4. Shashi Kant Mishra
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Corresponding author

Correspondence to Balendu Bhooshan Upadhyay .

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Editors and Affiliations

  1. Computer science and Applications Department, LGIPM, University of Lorraine, Metz Cedex 03, France

    Hoai An Le Thi

  2. Computer Science and Applications Department, LGIPM, University of Lorraine, Metz Cedex 03, France

    Hoai Minh Le

  3. Laboratory of Mathematics, National Institute for Applied Sciences (INSA)-Rouen Normadie, Saint-Étienne-du-Rouvray Cedex, France

    Tao Pham Dinh

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Upadhyay, B.B., Mishra, P., Mohapatra, R.N., Mishra, S.K. (2020). On the Applications of Nonsmooth Vector Optimization Problems to Solve Generalized Vector Variational Inequalities Using Convexificators. In: Le Thi, H., Le, H., Pham Dinh, T. (eds) Optimization of Complex Systems: Theory, Models, Algorithms and Applications. WCGO 2019. Advances in Intelligent Systems and Computing, vol 991. Springer, Cham. https://doi.org/10.1007/978-3-030-21803-4_66

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