GENERALIZED EXPONENTIAL PENALTY-FUNCTION FOR NONLINEAR-PROGRAMMING

Generalized exponential penalty functions are constructed for the multiplier methods in solving nonlinear programming problems. The nonsmooth extreme constraint g(ext) is replaced by a single smooth constraint g(s) by using the generalized exponential function (base a > 1). The approximation of g(s) to g(ext) can be refined by increasing the base a. The KS(x) function is found to be a special case of the proposed g(s) function (i.e. set a = e). A simple algorithm, using the proposed generalized exponential function g(s), is suggested for solving nonlinear programming problems. Both small and large-scale nonlinear programming problems (up to 2000 variables and 2000 nonlinear constraints) are solved to test the present algorithm.