This paper addresses a non-convex optimization problem, with the cost function and equality and inequality constraints defined by DC functions (difference of two convex functions).The main goal is to improve the Global Search Strategy (Scheme) (GSS) developed previously and to investigate its convergence. The latter requires the generalization of Global Optimality Conditions (GOCs). The paper presents the first version of such a transformation and, consequently, a new convergence proof for a modified GS strategy (with a weakened definition of resolving approximation), which is a combination of local search methods (LSM) and numerical procedures based on GOC, allowing to escape local minima and stationary points. In addition, within LSM, classical optimization methods can be used, as well as modern computational software. Note that the sequence produced by the GSS is minimizing for the limit problem \((\mathcal P_{**})\) , and when it is feasible, this sequence turns out to be minimizing for the original problem.