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arXiv · 2507.07674

An Adaptive Order Caputo Fractional Gradient Descent Method for Multi-objective Optimization Problems

Barsha Shaw·Md Abu Talhamainuddin Ansary
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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.

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Barsha Shaw, Md Abu Talhamainuddin Ansary. 2025-07-10. An Adaptive Order Caputo Fractional Gradient Descent Method for Multi-objective Optimization Problems. https://arxiv.org/abs/2507.07674

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