A modified Levenberg–Marquardt algorithm for low order-value optimization problem

Abstract

In this paper, we consider a modified Levenberg–Marquardt algorithm for Low Order Value Optimization problems(LOVO). In the algorithm, we obtain the search direction by a combination of LM steps and approximate LM steps, and solve the subproblems therein by QR decomposition or cholesky decomposition. We prove the global convergence of the algorithm theoretically and discuss the worst-case complexity of the algorithm. Numerical results show that the algorithm in this paper is superior in terms of number of iterations and computation time compared to both LM-LOVO and GN-LOVO algorithm.