Accelerated bundle level methods with inexact oracle

Abstract

In this paper, four accelerated bundle level methods are proposed to solve smooth and convex, smooth and strongly convex optimization problems and a class of saddle-point problems, respectively, by using the inexact first-order information of the objective functions. For each method two cases, where the accuracy of the oracle is chosen by the user and where the accuracy of the oracle is fixed in advance, are studied. The desired accuracy of the approximate solution and its corresponding iteration complexity of each proposed algorithm in each case are analyzed.