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