Some aspects of parallel and distributed iterative algorithms—A survey

A survey on the continuous nonlinear resource allocation problem

“…The most famous one is the successive projection method for polyhedral sets known as the Agmon-MotzkinSchoenberg algorithm [Agm54,MoS54]. Further examples can be found in the excellent surveys in [BeT89,BaB96,CeZ97]. Such methods can also in some cases be interpreted as subgradient methods for the minimization of a non-differentiable convex function over a closed convex set (e.g., [Gof78]), several methods for which also use projections onto level sets of convex functions or surrogate linearized subgradient inequalities (as in "poor man's bundle methods"); see, for example, the level methods in [LNN95,Kiw96a,Kiw96b], references found therein, and [Bra93, pp.…”

Partial regularization of the sum of two maximal monotone operators

“…The ability of dealing with nonsmoothness. The nice effect of the regularization on the decentralization of subproblems in the décomposition of large-scale programs (see [2], [10] and [15]). …”

“…In this sensé, it can be compared to similar approaches given in Bertsekas et aL [2] and in Spingarn [19]. Numerical experiments on these methods for the décomposition of large-scale convex programs will be published elsewhere.…”

An efficient algorithm for multiple simultaneous broadcasts in the hypercube

“…The simplest communication task involving broadcasting is the single node broadcast, where exactly one of the nodes wishes to broadcast a packet; see [BeT89]. This task can be accomplished in d time units, by using a spanning tree with shortest paths.…”

“…The single node broadcast is an extreme case of the problem analyzed in this note, corresponding to K = 1. The other extreme case, namely K = 2 d , corresponds to the multinode broadcast task, where all nodes wish to perform a broadcast at the same time; see (BeT89]. The minimum possible time for this task (in the dcube) is [2 -1] and it is attained by an algorithm by Bertsekas et al [BOSTT89].…”