Automatically retrieving information from images captured in low-light environments poses a significant challenge in computer vision. Various mathematical models based on Retinex theory have been proposed to enhance low-light images. However, the differentiability of the objective function has often been overlooked in these models. This study introduces a differentiable mathematical model with convex and linear constraints, termed Illumination Map Smoothing (IMS), designed to enhance the visual quality of recovered images by smoothing the initial illumination map and achieving a global optimum solution. Additionally, the proposed method corrects the illumination map using a simple linear transformation to increase the contrast and readability of enhanced images. This study also presents a heuristic approach to rapidly solve the proposed mathematical model with acceptable accuracy. The heuristic approach is suitable for image processing applications where low-light images must be enhanced without noticeable delay. To evaluate the performance of the proposed IMS method, it is compared with six existing approaches using various quantitative metrics and implementation times. The results indicate that the proposed IMS method outperforms other methods and is suitable for real-time applications.

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