The hyperbolic smoothing clustering method

It is considered the minimum sum-of-squares clustering problem. The mathematical modeling of this problem leads to a min − sum − min formulation which, in addition to its intrinsic bi-level nature, has the significant characteristic of being strongly non-differentiable. In order to overcome these difficulties, the resolution method proposed adopts a smoothing strategy using a special C∞ differentiable class function. The final solution is obtained by solving a sequence of low dimension differentiable unconstrained optimization subproblems which gradually approach the original problem. The use of this technique, called Hyperbolic Smoothing, allows the main difficulties presented by the original problem to be overcome. A simplified algorithm containing only the essential of the method is presented. For the purpose of illustrating both the reliability and the efficiency of the method, a set of computational experiments was performed making use of traditional test problems des...

• Type: Journal
• Year: 2010
• Where: PR
• Authors: Adilson Elias Xavier
• Keywords: Differentiable Unconstrained Optimization, Intrinsic Bi-level Nature, Original Problem, PR 2010