, Volume 55, Issue 1, pp 165–186 | Cite as

\(\chi\)-Optimal solution of single objective nonlinear optimization problem with uncertain parameters

  • Mrinal Jana
  • Geetanjali Panda
Theoretical Article


This paper addresses nonlinear optimization problem whose parameters are uncertain and lie in closed intervals. A partial ordering is introduced to define closeness between two intervals as well as two interval vectors. Existence of the solution of the model is studied using this partial ordering in case of unconstrained as well as constrained optimization problem. A variant of goal programming technique is used to develop a methodology to derive the solution. The methodology is illustrated through a numerical example. A possible application in finance is provided.


Nonlinear programming Interval valued function Interval inequality Order relation Goal programming 

Mathematics Subject Classification

90C29 90C31 90C46 90C90 



The authors are greatly indebted to the anonymous referees for valuable comments and remarks aimed at the improvement of the manuscript.


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Copyright information

© Operational Research Society of India 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Petroleum and Energy StudiesDehradunIndia
  2. 2.Department of MathematicsIndian Institute of Technology KharagpurKharagpurIndia

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