On Multi-objective Optimization Problems and Vector Variational-Like Inequalities

  • Vivek Laha
  • Harsh Narayan SinghEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 307)


This paper deals with nonsmooth multi-objective optimization problems involving locally Lipschitz \(V-r\)-invexity using Michel–Penot subdifferential. We consider vector variational-like inequalities of Stampacchia and Minty type and establish some results, which give necessary and sufficient conditions for a feasible point to be Pareto optimal solution of the MOP. We also establish various results related to weak Pareto optimal solution of the MOP and corresponding weak versions of the vector variational-like inequalities.


Multi-objective optimization Clarke subdifferential Michel–Penot subdifferential \(V-r\)-invexity Efficient solution Variational inequalities 



The research of the first author is supported by UGC-BSR start up grant by University Grant Commission, New Delhi, India (Letter No. F. 30-370/2017(BSR)) (Project No. M-14-40).


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© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Department of MathematicsInstitute of Science, Banaras Hindu UniversityVaranasiIndia

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