A Poximal-Projection Bundle Method for Convex Nonsmooth Optimization with On-Demand Accuracy Oracles
AbstractFor some practical problems, the exact computation of the function and (sub)gradient values may be difficult. In this paper, a proximal-projection bundle method for minimizing convex nonsmooth optimization problems with on-demand accuracy oracles is proposed. Our method essentially generalizes the work of Kiwiel (SIAM J Optim, 17: 1015-1034, 2006) from exact and inexact oracles to various oracles, including exact, inexact, partially inexact, asymptotically exact and partially asymptotically exact oracles. At each iteration, a proximal subproblem is solved to generate a linear model of the objective function, and then a projection subproblem is solved to obtain a trial point. Finally, global convergence of the algorithm is established under different types of inexactness.
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