A Symmetric Cone Proximal Multiplier Algorithm

This paper introduces a proximal multipliers algorithm to solve separable convex symmetric cone minimization problems subject to linear constraints. The algorithm is motivated by the method proposed by Sarmiento et al. (2016, optimization v.65, 2, 501-537), but we consider in the finite-dimensional vectorial spaces, further to an inner product, a Euclidean Jordan Algebra. Under some natural assumptions on convex analysis, it is demonstrated that all accumulation points of the primal-dual sequences generated by the algorithm are solutions to the problem and assuming strong assumptions on the generalized distances; we obtain the global convergence to a minimize point. To show the algorithm's functionality, we provide an application to find the optimal hyperplane in Support Vector Machine (SVM) for binary classification.