Saddle Point Criteria for Semi-infinite Programming Problems via an \(\eta \)-Approximation Method

  • Yadvendra Singh
  • S. K. Mishra
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 225)


In this paper, we consider a semi-infinite programming problem involving differentiable invex functions. We construct an \(\eta \)-approximated semi-infinite programming problem associated with the original semi-infinite programming problem and establish relationship between its saddle point and an optimal solution. We also establish relationship between an optimal solution of original semi-infinite programming problem and saddle point of \(\eta \)-approximated semi-infinite programming problem. Examples are given to illustrate the obtained results.


Semi-infinite programming Generalized convexity Optimality conditions 



The first author is supported by the Council of Scientific and Industrial Research(CSIR), New Delhi, India, through grant no. 09/013(0474)/2012-EMR-1.


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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.C.M.P. Degree College (A Constituent Postgraduate College of Central University of Allahabad)AllahabadIndia
  2. 2.Department of MathematicsInstitute of Science, Banaras Hindu UniversityVaranasiIndia

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