Exact penalty methods for minimizing of nonsmooth functions on convex sets

© 2015 Vladimir V. Karelin, Dmitry M. Lebedev and Lyudmila N. Polyakova.This paper considers a constrained nonsmooth optimization problem in which an objective function is locally Lipschitz and constraint func- tions are convex. With the help of exact penalty functions this problem is transformed into an unconstrained one. A regularity condition under which there exists an exact penalty parameters is introduced. For its implementation it is necessary that functions defining constraints were nonsmooth at every boundary point of this set. It is shown that in some cases it is possible to find an analytic representation of an exact penalty parameter.