clustering specification in a sense the process whereby this is achieved is an extension of a smoothing scheme called hyperbolic smoothing used in different contexts for solving nondifferentiable problems in general as presented in a b a santos u201c problemas de programa u00e7 u00e3o n u00e3o diferenci u00e1vel uma metodologia de suaviza u00e7 u00e3o u201d m sc thesis coppe ufrj rio de janeiro 1997 for solving the min max problem as presented in a m v chaves u201c resolu u00e7 u00e3o do problema minimax via suaviza u00e7 u00e3o u201d m sc thesis coppe ufrj rio de janeiro 1997 and for the covering of plane domains by circles as presented in a e xavier and a a f oliveira u201c optimal covering of plane domains by circles via hyperbolic smoothing u201d journal of global optimization 31 3 kluwer 2005 this technique was developed through an adaptation of the hyperbolic penalty method originally presented in a e xavier u201c penaliza u00e7 u00e3o hiperb u00f3lica urn novo m u0117todo para resolu u00e7 u00e3o de problemas de otimiza u00e7 u00e3o u201d m sc thesis coppe ufrj rio de janeiro 1982 by smoothing we fundamentally mean the substitution of an intrinsically nondifferentiable two level problem by a c u221e differentiable single level alternative this is achieved through the solution of a sequence.