A unified approach for inversion problems in intensity-modulated radiation therapy (IMRT) is proposed, combining dose and radiation source constraints in a single mathematical framework based on the split feasibility problem. The model does not impose an external objective function but instead minimizes a weighted proximity function measuring the sum of squared distances to the constraint sets. This ensures convergence to a feasible solution if the problem is consistent, or to a solution that minimally violates constraints otherwise. The algorithm is validated through computational results. IMRT involves delivering radiation beams through a multileaf collimator to target tumours, with constraints on dose distribution and beamlet intensities. The paper introduces equivalent uniform dose (EUD) as a clinical-relevant constraint, which is used alongside physical dose constraints. The unified model handles both EUD and physical dose constraints in a combined framework, extending to other dose constraints like dose-volume constraints. The split feasibility problem is formulated as finding a point in the intersection of constraint sets in two Euclidean spaces: beamlet intensity vectors and dose vectors. The model is solved using projection algorithms that minimize a weighted sum of proximity functions. The algorithm iteratively projects onto constraint sets, with the stepsize adjusted to ensure convergence. The algorithm is tested on a clinical case involving a thoracic tumour, demonstrating its effectiveness in achieving a feasible dose distribution. The results show that the algorithm converges efficiently, with the proximity function decreasing to a stopping criterion. The method is robust and handles inconsistent constraints by minimizing the violation of constraints. The approach is generalizable to other IMRT inversion problems where constraints are split between beamlet intensity and dose spaces. It avoids the need for matrix inversion, making it computationally efficient. The framework is supported by mathematical analysis and has potential applications in radiation therapy planning.A unified approach for inversion problems in intensity-modulated radiation therapy (IMRT) is proposed, combining dose and radiation source constraints in a single mathematical framework based on the split feasibility problem. The model does not impose an external objective function but instead minimizes a weighted proximity function measuring the sum of squared distances to the constraint sets. This ensures convergence to a feasible solution if the problem is consistent, or to a solution that minimally violates constraints otherwise. The algorithm is validated through computational results. IMRT involves delivering radiation beams through a multileaf collimator to target tumours, with constraints on dose distribution and beamlet intensities. The paper introduces equivalent uniform dose (EUD) as a clinical-relevant constraint, which is used alongside physical dose constraints. The unified model handles both EUD and physical dose constraints in a combined framework, extending to other dose constraints like dose-volume constraints. The split feasibility problem is formulated as finding a point in the intersection of constraint sets in two Euclidean spaces: beamlet intensity vectors and dose vectors. The model is solved using projection algorithms that minimize a weighted sum of proximity functions. The algorithm iteratively projects onto constraint sets, with the stepsize adjusted to ensure convergence. The algorithm is tested on a clinical case involving a thoracic tumour, demonstrating its effectiveness in achieving a feasible dose distribution. The results show that the algorithm converges efficiently, with the proximity function decreasing to a stopping criterion. The method is robust and handles inconsistent constraints by minimizing the violation of constraints. The approach is generalizable to other IMRT inversion problems where constraints are split between beamlet intensity and dose spaces. It avoids the need for matrix inversion, making it computationally efficient. The framework is supported by mathematical analysis and has potential applications in radiation therapy planning.