Alternated and Multi-Step Inertial Algorithm with Three-Term Conjugate Gradient-Like Direction for Split Feasibilities with Applications in Classification Problems and Elastic Net
摘要
In this work, we first introduce an alternated and multi-step inertial algorithm (AMiATTCG) for split feasibility problems in real Hilbert spaces. The suggested algorithm employs a three-term conjugate gradient-like direction, enabling faster convergence of its iterates toward a point in the solution set of the problem. The special point of the proposed method in this work is that it is the first method to combine conjugate gradient and general inertial methods in a single algorithm. Additionally, it is the first of its kind in the study of general inertial methods to integrate an alternated inertial term and a multi-step inertial term, both of which are improved versions of the classical inertial term. We establish the strong convergence of AMiATTCG by investigating the convergence of an alternated inertial relaxed algorithm with a three-term conjugate gradient-like direction and perturbations. Notably, our approach avoids some of the restrictive conditions commonly assumed in many methods with conjugate gradient-like directions, and the step-size used does not rely on any information about the norm of the underlying operator or the use of a line search. Moreover, we analyze the applications of the suggested method to classification problems based on the