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Illustration for DistributedOptimization
+form)%252C+where+%2524f_i%2524+and+%2524g_i%2524+are+potentially+nonsmooth.+The+agents+communicate+via+a+directed+graph+containing+%2524n%2524+nodes.+We+create+smooth+approximations+of+the+functions+%2524f_i%2524+and+%2524g_i%2524+and+develop+a+distributed+algorithm+utilizing+the+gradients+of+the+smooth+surrogates+and+a+finite-time+approximate+consensus+protocol.+We+term+this+algorithm+as+DDC-Consensus.+The+developed+DDC-Consensus+algorithm+allows+for+non-symmetric+directed+graph+topologies+and+can+be+synthesized+distributively.+We+establish+that+the+DDC-Consensus+algorithm+converges+to+a+stationary+point+of+the+nonconvex+distributed+optimization+problem.+The+performance+of+the+DDC-Consensus+algorithm+is+evaluated+via+a+simulation+study+to+solve+a+nonconvex+DC-regularized+distributed+least+squares+problem.+The+numerical+results+corroborate+the+efficacy+of+the+proposed+algorithm.&cdnurl=https%3a%2f%2fth.bing.com%2fth%2fid%2fR.ee7f0daf5afef879bf81da31d44cd20d%3frik%3dHp2bnxvNSuw8vg%26pid%3dImgRaw%26r%3d0&exph=630&expw=1200&q=Illustration+for+Distributed+Optimization&FORM=IRPRST&ck=D2BFD6F3A4EA60151D34BF84AEBC4B71&selectedIndex=17&itb=0)
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