Mixed-type duality approach for interval-valued programming problems with vanishing constraints

Abstract

In this article, we present a new mixed-type dual problem for the challenging class of the interval-valued optimization problem with vanishing constraints. The introduced dual problem does not directly include the index set, but it still requires calculations related to index sets, which makes it challenging to address these models from an algorithm perspective. The relationship between the original interval-valued programming problem with vanishing constraints and its mixed-type dual are discussed by weak, strong and strict converse duality theorems using the assumption of generalized convexity. We also present a non-trivial example to illustrate the theoretical aspects. Our proposed interval-valued mixed-type dual technique unifies the dual techniques discussed in Hu et al. (2020).