This talk is concerned with some algorithms based on the so-called maximum block improvement (MBI) method for non-convex block optimization. We mainly discuss its application in finding a Tucker decomposition for tensors. Traditionally, solution methods for Tucker decomposition presume that the size of the core tensor is specified in advance, which may not be a realistic assumption in some applications. Here we propose a new computational model where the configuration and the size of the core become a part of the decisions to be optimized. Also, we briefly mention its application in other fields, e.g., gene expression data, signal processing. Some numerical results will be presented.