The surface plasmon resonance (SPR) is known since the late 1950s. Its understanding was popularized by analytical models, in simple cases such as metallic plane plates between two dielectric media. The optimization of such structure for SPR biosensor applications is traditionally based on the minimization of the reflectance. Nevertheless this approach suffers from instabilities that require the limitation of the domain of search. An alternative formulation using the scattering matrix is proposed to improve the efficiency of optimization of this setup. The proposed model is mathematically rigorous and is coherent with the description of resonances in other fields of physics. The results of optimization and sensitivity analysis are discussed.