Levenberg–Marquardt-like algorithm with persistent iterations for solving low-order value optimization problems: a case study

Abstract In this study, we introduce a method for addressing fitting function determination problems through the framework of Low-Order Value Optimization (LOVO). Our approach is founded on the Levenberg–Marquardt algorithm, where, at each iteration, we aim to solve the minimization problem associated with a component function of the LOVO formulation. We designate this procedure as a persistent iteration. To evaluate the effectiveness of the proposed method, we present numerical results on geometric shape detection tasks, comparing its performance against established techniques for solving LOVO problems available in the literature. As a result of this work, we have an alternative method to those already established in the literature, which, in the context of fitting problems, demonstrates robust performance and, in general, reduces the number of objective function orderings in the associated LOVO problem.