A general method for the minimization of a class of nondifferentiable merit functions is presented. The merit functions are defined as the maximum absolute value of the components of a vector of functions. These merit functions have gradient discontinuities in the design space and cannot be minimized by efficient algorithms of mathematical programming. The technique consists of sequential minimizations of an appropriate family of substitute merit functions, namely, the pth order norm of the vector. The efficiency of the technique is illustrated by the design of continuous beams for optimum geometry and is shown to give good results. It is further indicated that the method could be applied to general nonlinear inequality constrained mathematical programming problems and a few encouraging numerical examples are presented.