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Error Bound property in mathematical programming

This article is devoted to the Error Bound property (also named R-regularity) in mathematical programming problems. This property plays an important role in analyzing the convergence of numerical optimization algorithms, a topic covered by multiple publications, and at the same time it is a relatively generic constraint qualification that guarantees the satisfaction of the necessary Kuhn – Tucker optimality conditions in mathematical programming problems. In the article, new sufficient conditions for the error bound property are described, and it’s also shown that several known necessary conditions are insufficient. The sufficient conditions obtained can be used to prove the regularity of a large class of sets including sets that cannot be proven regular by other known constraints.