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Abstract
This paper deals with quasidifferentiable vector optimization problems involving invex functions wrt convex compact sets. We present vector variational-like inequalities of Minty type and of Stampacchia type in terms of quasidifferentials denoted by (QMVVLI) and (QSVVLI), respectively. By utilizing these variational inequalities, we infer vital and adequate optimality conditions for an efficient solution of the quasidifferentiable vector optimization problem involving invex functions wrt convex compact sets. We also establish various results for the solutions of the corresponding weak versions of the vector variational-like inequalities in terms of quasidifferentials.
Acknowledgements
We are thankful to Prof. Amos Uderzo from Universit degli Studi di Milano-Bicocca for providing a suitable version of the mean value theorem which helped to prove some important results of this paper. We are also grateful to all the anonymous referees and the editor for their useful suggestions along with remarkable comments which helped to improve the quality of the paper.
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No potential conflict of interest was reported by the author(s).
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Notes on contributors
Harsh Narayan Singh
Harsh Narayan Singh is a M.Sc. in Mathematics and received his Ph.D. in Mathematics from the Department of Mathematics, Institute of Science, Banaras Hindu University in 2022. His research interests include multiobjective programming problems; mathematical programs with vanishing constraints; variational inequalities; generalised convexity; and related fields. He has published research papers in SCI and Scopus indexed international journals and conference proceedings. He has presented his research work in several national and international conferences.
Vivek Laha
Vivek Laha is working in the Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, India as an assistant professor since 2016. He has done his M.Sc. and Ph.D. in Mathematics from the same department in 2009 and 2014, respectively. He was awarded junior and senior research fellowships by the Council of Scientific and Industrial Research (CSIR) and postdoctoral fellowship by the National Board for Higher Mathematics (NBHM) under Government of India. He has completed a research project titled “Some applications of approximate convexity in recent optimization problems” supported by UGC-FRPS Start-Up Grant. He is a life member of the “Working Group on Generalized Convexity” and the “International Society on Multiple Criteria Decision Making”. His research interest lies in the fields of multiobjective optimization, variational inequalities, convex analysis, generalized convexity, nonsmooth analysis, mathematical programs with equilibrium/vanishing/swiching constraints, semi-infinite programming, semi-definite programming etc. He is a co-editor (with Prof. P. Marechal and Prof. S.K. Mishra) of a book titled “Optimization, Variational Analysis and Applications” published by Springer Singapore and a co-author of 7 book chapters. He has published 24 research articles till date in many international journals of high repute. He has successfully guided three research scholars for their Ph.D. degree. He is a reviewer for Mathematical Reviews by American Mathematical Society and a referee of several international journals. He has research connections in USA, Poland, France, Kuwait, Japan, Vietnam, Taipei etc. He has presented his research work in several national and international conferences both in India and abroad. He is working in different academic and administrative committees for his university.