Accuracy of protein-ligand binding free energy calculations utilizing implicit solvent models is critically affected by parameters of the underlying dielectric boundary, specifically, the atomic and water probe radii. Here, a global multidimensional optimization pipeline is developed to find optimal atomic radii specifically for protein-ligand binding calculations in implicit solvent. The computational pipeline has these three key components: (1) a massively parallel implementation of a deterministic global optimization algorithm (VTDIRECT95), (2) an accurate yet reasonably fast generalized Born implicit solvent model (GBNSR6), and (3) a novel robustness metric that helps distinguish between nearly degenerate local minima via a postprocessing step of the optimization. A graph-based "kT-connectivity" approach to explore and visualize the multidimensional energy landscape is proposed: local minima that can be reached from the global minimum without exceeding a given energy threshold (kT) are considered to be connected. As an illustration of the capabilities of the optimization pipeline, we apply it to find a global optimum in the space of just five radii: four atomic (O, H, N, and C) radii and water probe radius. The optimized radii, ρW = 1.37 Å, ρC = 1.40 Å, ρH = 1.55 Å, ρN = 2.35 Å, and ρO = 1.28 Å, lead to a closer agreement of electrostatic binding free energies with the explicit solvent reference than two commonly used sets of radii previously optimized for small molecules. At the same time, the ability of the optimizer to find the global optimum reveals fundamental limits of the common two-dielectric implicit solvation model: the computed electrostatic binding free energies are still almost 4 kcal/mol away from the explicit solvent reference. The proposed computational approach opens the possibility to further improve the accuracy of practical computational protocols for binding free energy calculations.