As there is a rapid development of the wearable camera embed glasses in this decade and these wearable camera embed glasses are portable for the consumer uses, many image recognition systems are developed based on these wearable camera embed glasses. To perform the image recognition, a deep learning based convolution neural network is employed. Instead of using the conventional back propagation approach for training the weight matrices in the convolution layer of the convolution neural network, this paper proposes an optimization approach for the design of these weight matrices. In particular, the error energy between the filtered input vectors and the desirable output vectors of the convolution layer as well as the Lp norm of the weight matrices are minimized subject to the frequency selectivity specifications imposed on these weight matrices. This design problem is actually a nonconvex functional inequality constrained sparse problem. Our recently developed sparse optimization method and nonconvex functional inequality constrained optimization method are applied for finding the solution of the optimization problem.