The detection of DNA copy number variants (CNVs) is essential for the diagnosis and prognosis of multiple diseases including cancer. Array-based comparative genomic hybridization (aCGH) is a technique to find these aberrations. The available methods for CNV discovery are often predicated on several critical assumptions based on which various regularizations are employed. However, most of the resulting problems are not differentiable and finding their optimums needs massive computations. This paper addresses a new entropic regularization, which is significantly fast and robust against various types of noises. The proposed problem takes advantage of the quadratic Renyi's entropy estimation which is not convex, but the half-quadratic programming gives an efficient solution with guaranteed convergence. We further theoretically prove that minimizing Renyi's entropy estimation would induce the sparsity and smoothness, two salient and desired features for recovered aCGH profiles. Extensive experimental results on simulated and real datasets illustrate the robustness and speed of the proposed method in comparison to the state-of-the-art algorithms.