A primal-dual approch to inexact subgradient methods

For optimization problems with computationally demanding objective functions and subgradients, inexact subgradient methods (IXS) have been introduced by using successive approximation schemes within subgradient optimization methods. This paper develops alternative solution procedures when the primal-dual information of IXS is utilized. This approach is especially useful when the projection operation onto the feasible set is difficult. The paper also demonstrates its applicability to stochastic linear programs.