Comparative study of RPSALG algorithm for convex semi-infinite programming

The Remez penalty and smoothing algorithm (RPSALG) is a unified framework for penalty and smoothing methods for solving min-max convex semi-infinite programing problems, whose convergence was analyzed in a previous paper of three of the authors. In this paper we consider a partial implementation of RPSALG for solving ordinary convex semi-infinite programming problems. Each iteration of RPSALG involves two types of auxiliary optimization problems: the first one consists of obtaining an approximate solution of some discretized convex problem, while the second one requires to solve a non-convex optimization problem involving the parametric constraints as objective function with the parameter as variable. In this paper we tackle the latter problem with a variant of the cutting angle method called ECAM, a global optimization procedure for solving Lipschitz programming problems. We implement different variants of RPSALG which are compared with the unique publicly available SIP solver, NSIPS, on a battery of test problems.

Music and movement: A comparative study between the BAPNE and Suzuki Methods

The aim of this article is to compare the Suzuki and BAPNE methods based on bibliography published for both approaches. In the field of musical and instrumental education and especially for the childhood stage, the correct use of the body and voice are of fundamental importance. These two methods differ from one another; one principally musical and instrumental, which is the Suzuki method, and one non-musical, the BAPNE method, which aims at stimulating attention, concentration, memory and the executing function of the pupil through music and body percussion. Comparing different approaches may provide teachers with a useful insight for facing different issues related to their discipline.