This approach is known as regularization, and deviations fromsolutions of the original problem are generally accepted as atrade-off for obtaining solutions with other desirable properties.
In fact, however, there exist necessary and sufficient conditions suchthat solutions of the regularized problem continue to be exactsolutions of the original problem. We present these conditions forgeneral convex programs, and give some applications of exactregularization.
(Joint work with Paul Tseng.)