Sufficient conditions for error bounds of difference functions and applications

This paper establishes verifiable sufficient conditions for the existence of error bounds for the sub‐level set of a difference function over an abstract constraint by applying a technique used by A. D. Ioffe. As a consequence, error bounds for constraint systems defined by d.c. inequalities and their applications in studying of exactness of the associated ${𝓁}_1$ penalty function and existence of Lagrange multipliers as necessary optimality conditions are also investigated.