Solving Split Pseudomonotone Equilibrium Problems with Multiple Output Sets: Applications in Machine Learning for Medical Diagnosis

We introduce a new class of split inverse problems, termed the Split Pseudomonotone Equilibrium Problem with Multiple Output Sets, which generalizes classical equilibrium formulations to accommodate multiple decision outputs and pseudomonotonicity. To solve this problem, we propose a novel iterative method that employs an inertial technique and self adaptive step sizes to improve the convergence properties. Under suitable conditions, we establish the convergence of the method and provide a detailed theoretical analysis. The proposed framework is then applied to medical diagnosis classification tasks, considering diabetes, chronic kidney disease, heart disease, and breast cancer datasets where decision making involves heterogeneous data. Numerical tests reveal the algorithm’s strength and effectiveness, underscoring its potential for wider use in optimization-based classification and decision-making systems.