An inexact proximal bundle method with applications to convex conic programming

We present an inexact bundle method for minimizing an unconstrained convex sup-function with an open domain. Under some mild assumptions, we reformulate a convex conic programming problem as such problem in terms of the support function. This method is a first-order method, hence it requires much less computational cost in each iteration than second-order approaches … Read more

Bundle Methods for Convex Minimization with Partially Inexact Oracles

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. We adapt this method 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 … Read more