Bundle methods for convex minimization with partially inexact oracles

Bibliografia s. 25-28

28 stron ; 21 cm

28 pages ; 21 cm

Recently the proximal bundle method for minimizing a convex function has been extended to an inexact oracle that delivers function and subgradient values of unknown accuracy. This method has been adapted to a partially inexact oracle that becomes exact only when an objective target level for a descent step is met. In Lagrangian relaxation, such oracles may save work by evaluating the dual function approximately on most iterations, without compromising the strong convergence properties of exact bundle methods. It was also shown that the recent method of Gaudioso et al. for finite min-max problems fits the partially inexact framework. In the work, its convergence results have been improved and useful modifications have been made. Numerical illustrations on stan­dard instances of the generalized assignment problem (GAP) are included.

Bibliography p. 25-28