*Result*: L1-Smooth SVM with Distributed Adaptive Proximal Stochastic Gradient Descent with Momentum for Fast Brain Tumor Detection.

*Brain tumors come in various types, each with distinct characteristics and treatment approaches, making manual detection a time-consuming and potentially ambiguous process. Brain tumor detection is a valuable tool for gaining a deeper understanding of tumors and improving treatment outcomes. Machine learning models have become key players in automating brain tumor detection. Gradient descent methods are the mainstream algorithms for solving machine learning models. In this paper, we propose a novel distributed proximal stochastic gradient descent approach to solve the L<subscript>1</subscript>-Smooth Support Vector Machine (SVM) classifier for brain tumor detection. Firstly, the smooth hinge loss is introduced to be used as the loss function of SVM. It avoids the issue of nondifferentiability at the zero point encountered by the traditional hinge loss function during gradient descent optimization. Secondly, the L<subscript>1</subscript> regularization method is employed to sparsify features and enhance the robustness of the model. Finally, adaptive proximal stochastic gradient descent (PGD) with momentum, and distributed adaptive PGD withmomentum(DPGD) are proposed and applied to the L<subscript>1</subscript>-Smooth SVM. Distributed computing is crucial in large-scale data analysis, with its value manifested in extending algorithms to distributed clusters, thus enabling more efficient processing ofmassive amounts of data. The DPGD algorithm leverages Spark, enabling full utilization of the computer's multi-core resources. Due to its sparsity induced by L<subscript>1</subscript> regularization on parameters, it exhibits significantly accelerated convergence speed. From the perspective of loss reduction, DPGD converges faster than PGD. The experimental results show that adaptive PGD withmomentumand its variants have achieved cutting-edge accuracy and efficiency in brain tumor detection. Frompre-trained models, both the PGD andDPGD outperform other models, boasting an accuracy of 95.21%. [ABSTRACT FROM AUTHOR]

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