Convergence Analysis of a New MaxMin-SOMO Algorithm

The convergence analysis of MaxMin-SOMO algorithm is presented. The SOM-based optimization (SOMO) is an optimization algorithm based on the self-organizing map (SOM) in order to find a winner in the network. Generally, through a competitive learning process, the SOMO algorithm searches for the minimum of an objective function. The MaxMin-SOMO algorithm is the generalization of SOMO with two winners for simultaneously finding two winning neurons i.e., first winner stands for minimum and second one for maximum of the objective function. In this paper, the convergence analysis of the MaxMin-SOMO is presented. More specifically, we prove that the distance between neurons decreases at each iteration and finally converge to zero. The work is verified with the experimental results.