This paper proposes a mathematical programming based approach for optimal estimation of photovoltaic cell model parameters. In this study, solar cell models are used to represent the current-voltage characteristics of the solar cell. The model is represented as a non-linear function that relates the cell current and voltage with some parameters to be estimated. No direct general analytical solution exists for such function. Given the input-output characteristic data of the solar cell, a mathematical programming technique is used to solve a set of transcendental equations to optimally estimate the solar cell parameters.