A generalization of interval-valued optimization problems and optimality conditions by using scalarization and subdifferentials

In this work, interval-valued optimization problems are considered. The ordering cone is used to generalize the interval-valued optimization problems on real topological vector spaces. Some definitions and their properties are obtained for intervals, defined via an ordering cone. Gerstewitz's function is used to derive scalarization for the interval-valued optimization problems. Also, two subdifferentials for interval-valued functions are introduced by using subgradients. Some necessary optimality conditions are obtained via subdifferentials and scalarization. An example is given to demonstrate the results.