Hearing aids suffer from the presence of a positive feedback loop between the output transducer and microphone. This feedback reduces both the stable gain achievable in the forward path as well as the sound quality of the output. Existing solutions to this problem perform feedback cancellation using adaptive filtering. The most common methods of adaptive filtering use the Least Mean Square (LMS) or Recursive Least Squares (RLS) algorithms, with the LMS being the most common choice for hearing aid applications. However, these approaches suffer from various drawbacks due to the unique challenges inherent in hearing aids. A new approach employing the Interior Point Least Squares (IPLS) algorithm demonstrates some distinct advantages over these other algorithms for use in the hearing aid schematic. Specifically, it is capable of achieving slightly faster convergence and, more significantly, maintains desired performance trade-offs with fixed parameter values despite changes in input signal power.