We propose an algorithm for the state feedback pole assignment problem. The algorithm is the first of its kind, making use of the Schur form and minimizing the departure from normality of the closed-loop poles by Newtons method. Eleven illustrative examples, comparing our algorithm with three other existing ones, are given.

The support vector machine (SVM) has been used in a wide variety of classification problems. The original SVM uses the hinge loss function, which is non-differentiable and makes the problem difficult to solve in particular for regularized SVMs, such as with 1 -regularization. This paper considers the Huberized SVM (HSVM), which uses a differentiable approximation of the hinge loss function. We first explore the use of the proximal gradient (PG) method to solving binary-class HSVM (B-HSVM) and then generalize it to multi-class HSVM (M-HSVM). Under strong convexity assumptions, we show that our algorithm converges linearly. In addition, we give a finite convergence result about the support of the solution, based on which we further accelerate the algorithm by a two-stage method. We present extensive numerical experiments on both synthetic and real datasets which demonstrate the superiority of our

This paper focuses on coordinate update methods, which are useful for solving problems involving large or high-dimensional datasets. They decompose a problem into simple subproblems, where each updates one, or a small block of, variables while fixing others. These methods can deal with linear and nonlinear mappings, smooth and nonsmooth functions, as well as convex and nonconvex problems. In addition, they are easy to parallelize.