This paper introduces a novel binary discriminative learning technique based on the approximation of the nonlinear decision boundary by a piecewise linear smooth additive model. The decision border is geometrically defined by means of the characterizing boundary points-points that belong to the optimal boundary under a certain notion of robustness. Based on these points, a set of locally robust linear classifiers is defined and assembled by means of a Tikhonov regularized optimization procedure in an additive model to create a final lambda-smooth decision rule. As a result, a very simple and robust classifier with a strong geometrical meaning and nonlinear behavior is obtained. The simplicity of the method allows its extension to cope with some of today's machine learning challenges, such as online learning, large-scale learning or parallelization, with linear computational complexity. We validate our approach on the UCI database, comparing with several state-of-the-art classification techniques. Finally, we apply our technique in online and large-scale scenarios and in six real-life computer vision and pattern recognition problems: gender recognition based on face images, intravascular ultrasound tissue classification, speed traffic sign detection, Chagas' disease myocardial damage severity detection, old musical scores clef classification, and action recognition using 3D accelerometer data from a wearable device. The results are promising and this paper opens a line of research that deserves further attention.