In this paper, we present an algorithm that simultaneously generates group-wise sparse attacks within semantically meaningful areas of an image. In each iteration, the core operation of our algorithm involves the optimization of a quasinorm adversarial loss. This optimization is achieved by employing the 1/2-quasinorm proximal operator for some iterations, a method tailored for nonconvex programming. Subsequently, the algorithm transitions to a projected Nesterov's accelerated gradient descent with 2-norm regularization applied to perturbation magnitudes. We rigorously evaluate the efficacy of our novel attack in both targeted and non-targeted attack scenarios, on CIFAR-10 and ImageNet datasets. When compared to state-of-the-art methods, our attack consistently results in a remarkable increase in group-wise sparsity, e.g., an increase of 48.12% on CIFAR-10 and 40.78% on ImageNet (average case, targeted attack), all while maintaining lower perturbation magnitudes. Notably, this performance is complemented by a significantly faster computation time and a 100% attack success rate.