Local search in problems with nonconvex constraints

Nonconvex optimization problems with an inequality constraint given by the difference of two convex functions (by a d.c. function) are considered. Two methods for finding local solutions to this problem are proposed that combine the solution of partially linearized problems and descent to a level surface of the d.c. function. The convergence of the methods is analyzed, and stopping criterions are proposed. The methods are compared by testing them in a numerical experiment.