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

2025/07/10 by Barsha Shaw, Shaw, Barsha, Md Abu Talhamainuddin Ansary +1 · 1 citation
Computer Science · Mathematics · #26A33 #49M05 #65K99 #90C25 #90C29 #Advanced Multi-Objective Optimization Algorithms #Advanced Optimization Algorithms Research #FOS: Mathematics #Metaheuristic Optimization Algorithms Research #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2507.07674

openalex publication_date 2025/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Generalized conditional gradient methods for multiobjective composite optimization problems with Hölder condition
• Smoothing Accelerated Proximal Gradient Method with Fast Convergence Rate for Nonsmooth Multi-objective Optimization
• Accelerating gradient descent and Adam via fractional gradients
• Regularized Evolution for Image Classifier Architecture Search
• Neural Networks Designing Neural Networks: Multi-Objective Hyper-Parameter Optimization
• A Fractional Model of Continuum Mechanics
• Gradient-based learning applied to document recognition

Cited by

• A Conjugate Gradient Method for Nonlinear Programming Problems using Caputo Fractional Gradients

Related

• A Conjugate Gradient Method for Nonlinear Programming Problems using Caputo Fractional Gradients
• A Caputo fractional derivative-based algorithm for optimization
• Enhancing Fractional Gradient Descent with Learned Optimizers
• Fast and Scalable Caputo Fractional Gradient Descent via Perturbation-Preserving Memory Compression
• The Novel Adaptive Fractional Order Gradient Decent Algorithms Design via Robust Control