Optimality and duality for second-order interval-valued variational problems

The paper studies the second-order interval-valued variational problem under η\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta $$\end{document}-bonvexity assumptions and proves the necessary optimality conditions. We investigate the functional which is η\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta $$\end{document}-bonvex but not invex. Further, we prove the duality theorems i.e. the weak and strong duality theorem to relate the values of the primal problem and dual problem. To validate the credibility of the weak duality theorem, we formulate an example of a second-order interval-valued variational problem.