Although numerous successful thermoacoustic refrigerators have been reported to date, the performance of these systems is still lower than their vapor compression counter parts. Optimization is imperative to identify the upper limit of the performance in order to be competitive and accepted by the general public. However, optimization methods adopted so far, experimentally and numerically, involved discrete variations of the selected parameters of interest. This paper presents the results of an optimization using the Lagrange Multiplier method, a mathematical approach never used before. The simultaneous optimization of the stack length and center position at various design temperatures is performed for a standard thermoacoustic refrigerator design. Results show similar pattern and trend with previous results with a 24.7% higher stack coefficient of performance achievable. This is promising considering that only two of the design parameters have been optimized.