{"ID":2896085,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.07674","arxiv_id":"2507.07674","title":"An Adaptive Order Caputo Fractional Gradient Descent Method for Multi-objective Optimization Problems","abstract":"This article introduces the multi-objective adaptive order Caputo fractional gradient descent (MOAOCFGD) algorithm for solving unconstrained multi-objective problems. The proposed method performs equally well for both smooth and non-smooth multi-objective optimization problems. Moreover, the proposed method does not require any a priori chosen parameters or ordering information of the objective functions. At every iteration of the proposed method, a subproblem is solved to identify a suitable descent direction toward an optimal solution. This subproblem involves an adaptive-order Caputo fractional gradient for each objective function. An Armijo-type line search is applied to determine a suitable step length. The convergence of this method for the Tikhonov-regularized solution is justified under mild assumptions. The proposed method is verified using different numerical problems, including neural networks.","short_abstract":"This article introduces the multi-objective adaptive order Caputo fractional gradient descent (MOAOCFGD) algorithm for solving unconstrained multi-objective problems. The proposed method performs equally well for both smooth and non-smooth multi-objective optimization problems. Moreover, the proposed method does not re...","url_abs":"https://arxiv.org/abs/2507.07674","url_pdf":"https://arxiv.org/pdf/2507.07674v1","authors":"[\"Barsha Shaw\",\"Md Abu Talhamainuddin Ansary\"]","published":"2025-07-10T11:54:13Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}