In the present paper, we focus our study on an interval-valued variational problem and derive sufficient optimality conditions by using the notion of invexity. In order to relate the primal interval-valued variational problem and its dual, several duality results, viz., weak, strong and converse duality results are established. Further, the Lagrangian function for the considered interval-valued variational problem is defined and we present some relations between an optimal solution of the considered interval-valued variational problem and a saddle point of the Lagrangian function. In order to illustrate the results proved in the paper, some examples of interval-valued variational problems have been formulated.
Bibliographical noteFunding Information:
The research of the first and third author is financially supported by King Fahd University of Petroleum and Minerals, Saudi Arabia under the Internal Research Project No. IN131026.
© 2018, The Natural Computing Applications Forum.
- Interval-valued problem
- LU optimal
ASJC Scopus subject areas
- Artificial Intelligence