Improved randomized approaches to the location of a conservative hyperplane

This paper presents improved approaches to the treatment of combinatorial challenges associated with the search process for conservative cuts arising in disjoint bilinear programming. We introduce a new randomized approach that leverages the active constraint information within a hyperplane containing the given local solution. It can restrict the search process to only one dimension and mitigate the impact of growing degeneracy imposed on computational loads. The utilization of recursion further refines our strategy by systematically reducing the number of adjacent vertices available for exchange. Extensive computational experiments validate that these approaches can significantly enhance computational efficiency to the scale of \(10^{-3}\) ${10}^{-3}$ s, particularly for those problems with high dimensions and degrees of degeneracy.