Industrial wastewater containing dye pollutants poses significant environmental challenges, necessitating advanced treatment technologies. This study presents the development and optimization of a novel PVDF/MgO mixed matrix membrane incorporating green-synthesized magnesium oxide nanoparticles using Arbutus unedo leaf extract for sustainable dye removal from aqueous solutions. The membrane's performance for Bemacid Turquoise dye removal was systematically optimized using three complementary approaches: Response Surface Methodology (RSM), artificial neural networks (ANN), and SOLVER algorithms. Comprehensive characterization was performed using X-ray diffraction, thermogravimetric analysis, Fourier-transform infrared spectroscopy, scanning electron microscopy, mechanical testing, and contact angle measurements. The optimum conditions were achieved with a membrane composition of 0.6 %, a temperature of 40 °C, and an initial dye concentration of 100 mg. L^-1. Comparative analysis revealed superior predictive accuracy of the ANN model over RSM, evidenced by lower mean squared error (MSE), mean absolute error (MAE), and root mean squared error (RMSE) values, coupled with higher R² correlation. SOLVER optimization further refined the parameters, achieving maximum Bemacid Turquoise removal at 94.08 mg/L initial concentration, 0.51 % membrane composition, and 50.12 °C temperature. The results demonstrate the exceptional potential of this eco-friendly PVDF/MgO membrane system as a sustainable and effective solution for industrial wastewater treatment, combining green synthesis principles with advanced optimization methodologies.