In convex nonsmooth optimization, it is known that the proximal bundle (PB) method has better practical performance than the subgradient method, since the whole historical information has been compressed to the current model. On the other hand, the subgradient method is known to possess the optimal iteration-complexity bound, however, the complexity estimate for the standard PB method is non-optimal. In this talk, we present a novel PB variant, namely, the relaxed proximal bundle (RPB) method, for solving convex nonsmooth composite optimization problems. Optimal iteration-complexity bounds for RPB are established for a large range of prox stepsizes, both in the convex and strongly convex settings.
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Jiaming Liang - is a Ph.D. student in Operations Research at Georgia Institute of Technology, under the supervision of Renato Monteiro. His research interests broadly include topics in optimization and algorithms, such as convex and nonconvex optimization, nonsmooth optimization, and high-dimensional sampling algorithms.