The $ F $-objective function method for differentiable interval-valued vector optimization problems

Abstract

<p style='text-indent:20px;'>In this paper, a differentiable vector optimization problem with the multiple interval-valued objective function and with both inequality and equality constraints is considered. The Karush-Kuhn-Tucker necessary optimality conditions are established for such a differentiable interval-valued multiobjective programming problem. Further, a new approach, called <inline-formula><tex-math id="M2">\begin{document}$ F $\end{document}</tex-math></inline-formula>-objective function method, is introduced for solving the considered differentiable vector optimization problem with the multiple interval-valued objective function. In this method, its associated vector optimization problem with the multiple interval-valued <inline-formula><tex-math id="M3">\begin{document}$ F $\end{document}</tex-math></inline-formula>-objective function is constructed. Their equivalence is established under <inline-formula><tex-math id="M4">\begin{document}$ F $\end{document}</tex-math></inline-formula>-convexity assumptions. It is shown that the introduced approach can be used to solve a nonlinear nonconvex interval-valued optimization problem. By using the introduced approximation method, it is also presented in some cases that a nonlinear nonconvex interval-valued optimization problem can be solved by the help of methods for solving linear interval-valued optimization problems.