Distributed Randomized Gradient-Free Mirror Descent Algorithm for Constrained Optimization

This article is concerned with the multiagent optimization problem. A distributed randomized gradient-free mirror descent (DRGFMD) method developed by introducing a oracle in scheme where non-Euclidean Bregman divergence used. The classical gradient generalized without using subgradient information of objective functions. proposed algorithms are first zeroth-order methods, which achieve an approximate $O(\frac{1}{\sqrt{T}})$ notation="LaTeX">$T$-rate convergence, recovering best known optimal rate nonsmooth constrained convex optimization. Moreover, decentralized reciprocal weighted averaging (RWA) approximating sequence investigated, convergence for RWA shown to hold over time-varying graph. Rates comprehensively explored algorithm (DRGFMD-RWA). technique on constructing provides new insight searching minimizers algorithms.