On fully distributed dual first order methods for convex network optimization

Decentralized optimization methods for solving social profit optimization problems in electricity market

“…On the other hand, to optimize the social profit with cooperative agents, as a widely discussed optimization framework, each agent maintains an individual decision variable and the optimal solution of the whole market can be achieved through multiple rounds of decision-making [18]. When considering the asynchronous factors in the practical systems, the existing algorithms only applicable to synchronous systems may be restrictive [18][19][20][21][22][23][24][25][26][27]. To deal with the asynchrony, existing asynchronous optimization algorithms can be found in [28][29][30][31][32][33][34][35][36], which were developed based on the prior knowledge of the probability distribution of asynchronous factors.…”

“…and proximal gradient method [117], etc. Optimization problems with coupling constraints are actively investigated in the recent works [18][19][20][21][22][23][24][25][26][27], where the optimal solution to the primal problems is usually achieved with the update of both primal and dual variables. An alternative solution, as discussed in [45,46], is resorting to the dual problems, where the computation on the primal variables is not required.…”

“…Furthermore, if the proximal mapping of the non-smooth parts in the primal problem can be explicitly derived, we only need to update the dual variables by some simple operations (e.g., addition, multiplication, and Euclidean projection) without inner-loop optimizations [18,[20][21][22][23][24]26]. 1 In addition, the asymmetric individual interpretations of the coupling constraints are considered, where no uniform knowledge of the coupling constraints is required.…”