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On local search in d.c. optimization

This paper addresses a nonconvex optimization problem with the cost function and inequality constraints given by d.c. functions. The original problem is reduced to a problem without inequality constraints by the exact penalization procedure. A special local search method for the penalized problem is developed, which is based, first, on the linearization procedure with respect to the basic nonconvexity and, second, on the consecutive solutions of linearized convex problems. Convergence properties of the method are investigated. Finally, a preliminary computational testing of the local search method developed has been carried out on several test problems taken from literature.