An algorithm to solve polytopic set optimization problem based on a partial set order relation

The primary aim of this paper is to present an algorithm for computing a weak \(m\) $m$ -minimizer and an \(m\) $m$ -minimizer for a class of set optimization problems. The solution concepts are based on \(m\) $m$ -order relation proposed by Karaman et al. (Positivity 22:783–802, 2018). The \(m\) $m$ -order relation is initially characterized in terms of support functions. Two scalar optimization problems are formulated to derive optimality conditions for weak \(m\) $m$ -minimizers and \(m\) $m$ -minimizers. Subsequently, the algorithm presented by Löhne and Schrage (Optimization 64(9):2039–2041, 2015) is modified to develop the algorithm. The paper includes numerical examples to validate the algorithm.