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We study the problem of multiway number partition optimization, which has amyriad of applications in the decision, learning and optimization literature.Even though the original multiway partitioning problem is NP-hard and requiresexponential time complexity algorithms; we formulate an easier optimizationproblem, where our goal is to find a solution that is locally optimal. Wepropose a linearithmic time complexity $O(N\log N)$ algorithm that can producesuch a locally optimal solution. Our method is robust against the input andrequires neither positive nor integer inputs.

A Linearithmic Time Locally Optimal Algorithm for the Multiway Number Partition Optimization