Exact penalty methods for nonsmooth optimization

Methods of penalty functions are widely used in nonlinear programming. The idea of penalty function methods consists in reducing the problem of conditional optimization to a problem of the unconstrained optimization. Among the different approaches existing for such reduction we shall consider the method of exact penalty nondifferentiable functions. The implementation of exact penalty function methods first of all depends on the properties of an objective function and a function defining a constraint. Therefore various conditions are imposed on these functions to make it possible to solve our problem.