A diagonal quasi-Newton method for unconstrained multiobjective optimization

Multiobjective optimization has become increasingly important in modern computational science, particularly in artificial intelligence and financial modelling. To address this challenge, we propose a novel diagonal BFGS quasi-Newton method for unconstrained multiobjective optimization. First, we develop an efficient diagonal matrix updating process to approximate the Hessian matrix for each objective function. Then, we theoretically analyze the descent direction properties and implement the method with both Armijo and Wolfe line search strategies. Finally, we rigorously establish the algorithm's global convergence under mild assumptions. Extensive numerical experiments demonstrate that our method outperforms conventional approaches, achieving significant improvements in computational efficiency and convergence behaviour.