Journal of Optimization Theory and Applications

, Volume 156, Issue 2, pp 278–293 | Cite as

On Approximately Star-Shaped Functions and Approximate Vector Variational Inequalities

  • S. K. Mishra
  • Vivek Laha


In this paper, we consider a vector optimization problem involving approximately star-shaped functions. We formulate approximate vector variational inequalities in terms of Fréchet subdifferentials and solve the vector optimization problem. Under the assumptions of approximately straight functions, we establish necessary and sufficient conditions for a solution of approximate vector variational inequality to be an approximate efficient solution of the vector optimization problem. We also consider the corresponding weak versions of the approximate vector variational inequalities and establish various results for approximate weak efficient solutions.


Approximately star-shaped functions Fréchet subdifferentials Approximate vector variational inequalities Approximate efficient solutions Approximately straight functions 



The research of the second author is supported by the Council of Scientific and Industrial Research, New Delhi, Ministry of Human Resources Development, Government of India Grant 20-06/2010 (i) EU-IV.


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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceBanaras Hindu UniversityVaranasiIndia

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