An Adaptive Order Caputo Fractional Gradient Descent Method for Multi-objective Optimization Problems
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918088268578816 |
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| author | Shaw, Barsha Ansary, Md Abu Talhamainuddin |
| author_facet | Shaw, Barsha Ansary, Md Abu Talhamainuddin |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_07674 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Adaptive Order Caputo Fractional Gradient Descent Method for Multi-objective Optimization Problems Shaw, Barsha Ansary, Md Abu Talhamainuddin Optimization and Control 26A33, 90C29, 90C25, 65K99, 49M05 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. |
| title | An Adaptive Order Caputo Fractional Gradient Descent Method for Multi-objective Optimization Problems |
| topic | Optimization and Control 26A33, 90C29, 90C25, 65K99, 49M05 |
| url | https://arxiv.org/abs/2507.07674 |