Low-light photography conditions degrade image quality. This study proposes a novel Retinex-based low-light enhancement method to correctly decompose an input image into reflectance and illumination. Subsequently, we can improve the viewing experience by adjusting the illumination using intensity and contrast enhancement. Because image decomposition is a highly ill-posed problem, constraints must be properly imposed on the optimization framework. To meet the criteria of ideal Retinex decomposition, we design a nonconvex $L_{p}$ norm and apply shrinkage mapping to the illumination layer. In addition, edge-preserving filters are introduced using the plug-and-play technique to improve illumination. Pixel-wise weights based on variance and image gradients are adopted to suppress noise and preserve details in the reflectance layer. We choose the alternating direction method of multipliers (ADMM) to solve the problem efficiently. Experimental results on several challenging low-light datasets show that our proposed method can more effectively enhance image brightness as compared with state-of-the-art methods. In addition to subjective observations, the proposed method also achieved competitive performance in objective image quality assessments.